Question

How do you differentiate `f(x) = sqrt(arctan(2x^3)` using the chain rule?

Answer 1

`f’(x) = (3x^2) / ((1+4x^6)(sqrt(arctan(2x^3)))`

Explanation:

`f(x) = sqrt(arctan(2x^3))`

`f’(x) = (1/(2sqrt(arctan(2x^3))) * 1/(1+(2x^3)^2) * (6x^2))`

`= (3x^2) / ((1+4x^6)(sqrt(arctan(2x^3)))`