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How do you differentiate #f(x)=cot(e^(x)) # using the chain rule?

1 Answer

Harish Chandra Rajpoot

Jul 16, 2018

#f'(x)=-e^x\cosec^2(e^x)#

Explanation:

Given function:

#f(x)=\cot(e^x)#

#\frac{d}{dx}f(x)=frac{d}{dx}(\cot (e^x))#

#f'(x)=-\cosec^2 (e^x)\frac{d}{dx}(e^x)#

#=-\cosec^2 (e^x)(e^x)#

#=-e^x\cosec^2(e^x)#

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