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

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Answer 1 · 2018-04-05T01:18:29

#f'(x)=-sec^2(1/x)/x^2#

#f(x)=tan(1/x)#

#f(x)=tan(x^-1)#

Now, when applying the Chain Rule to the tangent function, where #u# is a function,

#d/dxtan(u)=sec^2(u)(du)/dx#

Thus,

#f'(x)=sec^2(1/x)*d/dxx^-1#

#f'(x)=-sec^2(1/x)/x^2#