What is the derivative of $f (x) = {tan}^{- 1} (e^{x})$ $f(x)=tan^-1(e^x)$ ?

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Answer 1 · 2014-08-30T14:20:25

By Chain Rule, we can find $f'(x)=frac{e^x}{1+e^{2x}}$ .

Note: $[tan^{-1}(x)]'={1}/{1+x^2}$ .

By Chain Rule,
$f'(x)={1}/{1+(e^x)^2}cdot e^x={e^x}/{1+e^{2x}}$

What is the derivative of f(x)=tan^-1(e^x)f(x)=tan−1(ex)f(x)=tan^-1(e^x) ?