Question

What is the derivative of `y = sin(tan(5x))`?

Answer 1

`y'=5sec^2(5x)cos(tan(5x))`

Explanation:

Use the chain rule. The first overriding issue is the tangent function inside the sine function.

`y'=cos(tan(5x))d/dx[tan(5x)]`

Next, use chain rule again to find the derivative of the tangent function.

`d/dx[tan(5x)]=sec^2 5xd/dx[5x]=5sec^2(5x)`

Multiply this back in to find `y'`.

`y'=5sec^2(5x)cos(tan(5x))`