Question

How do you differentiate `sqrt(sin^3(1/x^2)` using the chain rule?

Answer 1

Always convert to exponents first ...

Explanation:

`d/(dx)[(sin(x^-2))^3]^(1/2)`

`=(1/2)[(sin(x^-2))^3]^(-1/2)(3)(sin(x^-2))^2(cos(x^-2))(-2x^-3)`

`=-3x^-3[(sin(x^-2))^3]^(-1/2)(sin(x^-2))^2(cos(x^-2))`

hope that helped