Question

How do you find the derivative of `F(X)= tan^-1(E^(x*sinx))`?

Answer 1

`((sinx + x cos x)e^(x sin x))/(1+e^(2x sin x)`

Explanation:

Use function of function of function rule.

`F'=(1/(1+(e^(x sin x)) ^2)){(e^(x sin x))'}`

`=(1/(1+e^(2x sin x)))e^(x sin x){(x sin x)'}`

`=(1/(1+(e^(2x sin x))))e^(x sin x)(sin x + x cos x)`

`=((sinx + x cos x)e^(x sin x))/(1+e^(2x sin x)`