Let f(x)=(tan^-1x)^4. Find f'(x)

Question

The webwork system will accept arctan(x) and not tan^-1(x) as the inverse of tan(x)

Answer 1

Use the chain rule. The derivative of the outside function is 4(tan^-1(x))³. The derivative of the inside function is 1/(1+x²) So f'(x) = 4(tan^-1(x))³/(1+x²)

Answer 2

We are given f(x) = (arctan(x))^4

The derivative is therefore

df(x)/dx = 4 * (arctan(x))^3 * (d(arctan(x))/dx)

= 4 * (arctan(x))^3 / (1 + x^2)