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

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Answer 1 · 2016-07-01T04:18:04

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

Use function of function of function rule.

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

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

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

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

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