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

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Aug 30, 2014

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}}#

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