Question

What is the derivative of `(x^4+3x^2-2)^5`?

Answer 1

The derivative is `5(x^4+3x^2-2)^{4} * (4x^3+6x)`.

Explanation:

The Chain Rule says `d/dx(f(g(x))) = f'(g(x)) * g'(x)`. For the function `(x^4+3x^2-2)^5`, use `f(x)=x^5` and `g(x)=x^4+3x^2-2`. Then `f'(x)=5x^4` and `g'(x)=4x^3+6x`. Therefore, `d/dx((x^4+3x^2-2)^5)=5(x^4+3x^2-2)^{4} * (4x^3+6x)`.