Question

What is the derivative of `tan(1/x)`?

Answer 1

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

Explanation:

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

`d/dx(tanx)=sec^2x`

`•color(white)(x)d/dx(tan(f(x)))=sec^2(f(x))xxf'(x)`

`f(x)=1/x=x^-1rArrf'(x)=-1x^-2=-1/x^2`

`rArrd/dx(tan(1/x))=sec^2(1/x)xx-1/x^2`

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