Question

How do you differentiate `sqrt(sin^2(1/x)` using the chain rule?

Answer 1

`f^'(x)=-1/(2 x^2*sqrt ((sin^2(1/x)))) * sin(2/x)`

Explanation:

`f(x)=sqrt(sin^2(1/x))= (sin^2(1/x))^(1/2)`

`f^'(x)=1/2(sin^2(1/x))^(-1/2)* 2 sin(1/x)* cos(1/x)* -1/x^2`

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

`f^'(x)=-1/(2x^2*sqrt((sin^2(1/x)))) * sin(2/x)` [Ans]