How do you differentiate #f(x)=cot(e^(1/x)) # using the chain rule?

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Answer 1 · 2018-07-12T20:21:30

#f'(x)=-\frac{e^{1/x}cosec^2(e^{1/x})}{x^2}#

Given function:

#f(x)=\cot(e^{1/x})#

differentiating above function w.r.t #x# using chain rule as follows

#\frac{d}{dx}f(x)=\frac{d}{dx}\cot (e^{1/x})#

#f'(x)=-cosec^2(e^{1/x})\frac{d}{dx}(e^{1/x})#

#=-cosec^2(e^{1/x})\cdot e^{1/x}\frac{d}{dx}(1/x)#

#=-cosec^2(e^{1/x})\cdot e^{1/x}(-1/x^2)#

#=-\frac{e^{1/x}cosec^2(e^{1/x})}{x^2}#