<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Tue, 21 Apr 2026 04:05:40 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/dtube-calculus/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[DTube: Integral of sin^3(x), sin^3(ax) with substitution and trigonometric identity]]></title><description><![CDATA[In this tutorial, we'll work through 2 different approaches to solving the integral of sin3(ax). Now, there maybe more ways of approaching this problem, but these were the most obvious to me. Using a]]></description><link>http://direct.ecency.com/dtube/@masterwu/ech208ff</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/ech208ff</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Sat, 07 Oct 2017 09:16:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/B69zEhWZA8UBY9hoU8oh9J4ApKv6igLVANrFdPra54ryiNVKfg79WGzz9mVWXZpL4QPq6tVNPfLTG4ZzGroaNFRu87Z47B9um2pgkWsQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: The math behind your Camping Torch with dy/dx = -ky]]></title><description><![CDATA[We can apply the principle of exponential decay to find equations that model the charge remaining in a capacitor as it is discharged through a resistor. The circuit diagram is shown below... When the switch]]></description><link>http://direct.ecency.com/dtube/@masterwu/e8dwjhui</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/e8dwjhui</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Wed, 27 Sep 2017 12:45:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMDkLA8sZndHNkETF8z8qJ366MvBDoWjN77pxKHvmUCnk12zEPiFMPC1yfAz9T?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Integral of ∫√(a^2 - x^2)dx using a Trigonometric Substitution]]></title><description><![CDATA[What I love about mathematics is some of the very creative and ingenious methods that someone has come up with to find solutions to perplexing problems. The integral of √(a2 - x2) is a great example one]]></description><link>http://direct.ecency.com/dtube/@masterwu/6dfqg3vt</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/6dfqg3vt</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Mon, 25 Sep 2017 04:31:24 GMT</pubDate><enclosure url="https://images.ecency.com/p/3HaJVw3AYyXBD5Md5tUD9YKkzGo1eoR2RP1hYxRaFr2EXB72vfAiySio3Zxy6nibxqrieivtwxok6SfUSvfZYEbQMHgcgUmv7M2A9Ep?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Modelling the Decay of Nuclear Medicine with dy/dx = -ky]]></title><description><![CDATA[Inasmuch as the differential equation dy/dx = ky models exponential growth, it follows that dy/dx = -ky models exponentially decaying processes. A exponential decay process, which is a slowing reduction]]></description><link>http://direct.ecency.com/dtube/@masterwu/0csyorjj</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/0csyorjj</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Sat, 23 Sep 2017 06:11:33 GMT</pubDate><enclosure url="https://images.ecency.com/p/B69zEhWZA8UBY9hoU8oh9J4ApKv6igLVANrFdPra54ryhkkKqMdi8QVCCwbtt82QfYTSHhgeyHB7FRQpFzR7xGU3Dkrqd6JCQu1cAXTe?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Modelling Exponential Growth of Bacteria with dy/dx = ky]]></title><description><![CDATA[With the differential equation dy/dx = ky, we found the general solution to be y(x) = Aekx. We worked this out in my last post. This equation lends itself to the modelling of exponential growth. Now in]]></description><link>http://direct.ecency.com/dtube/@masterwu/sytggy1z</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/sytggy1z</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Wed, 20 Sep 2017 03:50:24 GMT</pubDate><enclosure url="https://images.ecency.com/p/Zskj9C56UonYARCqq1q4rLKupB1bvXrZSNGB7jRc4Z6a4TKY7HDHNdxGJes8sMBnBqZYcXMdPrXCFQE7ANCQy1v7Yjyb82x1Wf22wqxj6CrB2pq1Ep3J?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Separable Differential Equations: dy/dx = ky]]></title><description><![CDATA[In this video, we work through the process of solving for the general solution of a simple separable differential equation: The general solution is obtained by separating the variables so that all y's]]></description><link>http://direct.ecency.com/dtube/@masterwu/t1u63l9n</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/t1u63l9n</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Sun, 17 Sep 2017 05:42:12 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMCn3vwD3S3EXMVXQGgbMLTxPGr6vBc1BgKXNyTRztXvKkTmwX5vCV5eb2XdJD?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Introduction to Differential Equations]]></title><description><![CDATA[Differential Equations are one of the most useful tools developed in mathematics. You'll see them everywhere in Engineering, Physics, Biology, etc. for the modelling of phenomena. So what are differential]]></description><link>http://direct.ecency.com/dtube/@masterwu/9supff9u</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/9supff9u</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Wed, 13 Sep 2017 12:12:39 GMT</pubDate><enclosure url="https://images.ecency.com/p/mXkfdToSwHy8jids4vLdR7JmGKicDFWgZWnhwA45mXrH5PMjxrerZiST7682czgR1CRaNnMsQmBAggojnu58BhxqDme8Zr37g8FN8tFkT?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Integral of ∫1/(a^2 + x^2)]]></title><description><![CDATA[The term 1/(a2 + x2) is purely algebraic. However, its integral is trigonometric. When you look this up in a table of integrals, you'll find the integral: ∫1/(a2+x2)dx = (1/a)arctan(x/a) + C How is this]]></description><link>http://direct.ecency.com/dtube/@masterwu/opmezzlv</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/opmezzlv</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Tue, 12 Sep 2017 15:12:45 GMT</pubDate><enclosure url="https://images.ecency.com/p/6VvuHGsoU2QBxYFFLuywjgtJfwdjbpYkoiukQZZHzkRSVx7DCEGGnSS2btCodwNdZVQ5UDcQocC23hgM3xPesm5imwzfieHSuFFyEcXsVwfq3ZsYWcjYZPVKWyyafj?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Reduction Formula for Integral of ∫cos^n(x)dx]]></title><description><![CDATA[In this video, we work through the derivation of the reduction formula for the integral of cosn(x) or [cos(x)]n. The first step is to rewrite the integral as: ∫cosn(x)dx = ∫cosn-1(x)cos(x)dx Thus we have]]></description><link>http://direct.ecency.com/dtube/@masterwu/tfqrboxd</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/tfqrboxd</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Mon, 11 Sep 2017 15:26:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMD9sGwe1EFPiKfGomwhbjXPCCfotzmUT6WdNTtQXVkRn8KHa3rcZ2roaT5E42?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[DTube: Integral of ∫cos^3(x)dx]]></title><description><![CDATA[In this video, I work through the steps to solving the integral of cos3(x) or [cos(x)]3. Note that because cos(x) is a function of x, not a mere polynomial, we can't just use the power formula as a method]]></description><link>http://direct.ecency.com/dtube/@masterwu/vwv5n7k6</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@masterwu/vwv5n7k6</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[masterwu]]></dc:creator><pubDate>Sat, 09 Sep 2017 10:25:45 GMT</pubDate><enclosure url="https://images.ecency.com/p/6VvuHGsoU2QBxYFFLuywjgtJfwdjbpYkoiukQZZHzkRSVx7DCEGGnSS2btCodwNdZVR5DgUtJGQE5xp3bwgpJysKeFvSt2b6CwesEcuMXa1U7hTJLF1ab26Zochxyo?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Exponents Part One - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivatives of Exponents Part One - A Calculus Math Tutorial video on DTubeIn this excerpt from the derivatives of whole number exponents (1,2,3,4,5.....) are explained through geometry. This short]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/iujud42g</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/iujud42g</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:29:27 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMCkwg9wPYG5ST4HZD7LB3gJxFG4a1MQV2b2hrEReryY78dw1KGoRwcaRkhKUC?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivative of an Inverse Function - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivative of an Inverse Function - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function which is an inverse of some original function. This short but very]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/r8vfx2oe</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/r8vfx2oe</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:23:48 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMD6mEPJssDuB6YtwvPtrXb9TEmtBaKNoBm4xVQPDSSKFSWcyn5ZxSx1Dk1xzS?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Functions Within Functions - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivatives of Functions Within Functions - A Calculus Math Tutorial video on DTubeExcerpt from In this brief video the derivatives of functions within functions are described through geometry. This]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/vrfr4d7y</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/vrfr4d7y</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:17:33 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCM8HH2oxTWE3mMbbWuFFJPyjgPkNbSMMP5gJjYhJCBSwF2PdiZNm6DoYHhJKgX?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Division - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivatives of Division - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two divided functions is explained through geometry. This]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/znz0jp0f</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/znz0jp0f</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:11:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCM8tCgm9aVD6iWzhJSvxibDrc5S2fUKkmWwKr9nTiEnsh6iJMnGgAyFgZaJbJU?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Multiplication - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivatives of Multiplication - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two multiplied functions is explained through geometry.]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/i2x0vv6m</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/i2x0vv6m</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:06:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCM8HD7JHEUajkqUB1CVZ66WU3BP4D57eYWbRwMe2CPMp8s2kgxZ5VzaX9SY5o7?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Sin, Cos, Tan Trigonometry - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Derivatives of Sin, Cos, Tan Trigonometry - A Calculus Math Tutorial video on DTubeIn this excerpt from a derivatives of trigonometric functions sin, cos, and tan are explained through geometry.]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/gu3rpxeg</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/gu3rpxeg</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 11:00:57 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCM7FgHkdDBPyZLC1g2ZoBeYuaJyKMGXfABAQTfovzSdYKxjeHBLed5idrKYaWY?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition of Derivatives - A Calculus Math Tutorial]]></title><description><![CDATA[Watch Definition of Derivatives - A Calculus Math Tutorial video on DTubeIn this excerpt from the definition of the derivative is described through geometry. Derivatives are a basic concept of calculus]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/sgjh4bj1</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/sgjh4bj1</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 10:55:39 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCM9BMxvVhXANavpVGfW5rLJp7J38g31AXFrkQ7t9fht1kFcXCoygYxZKb7ZNrM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives of Addition - A Calculus Math Tutorial ]]></title><description><![CDATA[Watch Derivatives of Addition - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two added functions is explained through geometry. This]]></description><link>http://direct.ecency.com/dtube/@eroavromninocule/1xkde0sy</link><guid isPermaLink="true">http://direct.ecency.com/dtube/@eroavromninocule/1xkde0sy</guid><category><![CDATA[dtube]]></category><dc:creator><![CDATA[eroavromninocule]]></dc:creator><pubDate>Sat, 19 Aug 2017 10:50:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwzwxM6L1P6uLNceBDDCMACSSwNYx8GFP9CpqoPdHdUTC9Y4jJ34v3v2NxUXhso4f7bHobZcqhH6fcUM3?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>