Question

What is the derivative of this function `y=tan^-1(x^3)-x`?

Answer 1

`dy/dx = (3x^2)/(x^6+1)-1`

Explanation:

`y = arctan(x^3)-x`

`dy/dx= 1/((x^3)^2+1) * d/dx(x^3) -d/dx x` (Standard differential and chain rule)

`= 1/(x^6+1) * 3x^2 -1` (Power rule)

`= (3x^2)/(x^6+1)-1`