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

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

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

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

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

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

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