How do you find the derivative of tan(1/x)tan(1x)?

1 Answer
Jim G.
Oct 3, 2017

-(sec^2(1/x))/x^2=-1/x^2sec^2(1/x)−sec2(1x)x2=−1x2sec2(1x)

Explanation:

"differentiate using the "color(blue)"chain rule"differentiate using the chain rule

"given "y=f(g(x))" then"given y=f(g(x)) then

dy/dx=f'(g(x))xxg'(x)larr" chain rule"

rArrd/dx(tan(1/x))

=sec^2(1/x)xxd/dx(x^-1)

=sec^2(1/x)xx-x^-2

=-(sec^2(1/x))/x^2=-1/x^2sec^2(1/x)

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