`y = e^(2x) tan(2x)` Find the derivative.

Sunday, August 31, 2014

Find the derivative if `y=e^(2x)tan(2x) ` :

Let u=2x and rewrite as:

`y=e^utanu `

Use the product rule noting that `d/(du)e^u=e^udu,d/(du)tanu=sec^2udu ` :

`(dy)/(du)=e^udutanu+e^usec^2udu `

Since u=2x, du=2 so we can rewrite as:

`(dy)/(dx)=2e^(2x)tan(2x)+2e^(2x)sec^(2)2x `

` (dy)/(dx)=2e^(2x)(tan(2x)+sec^2(2x)) `

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