Question

If f(x) = (x+1)(x^2-2)^3 then f'(x)

Answer 1

(x^2-2)^2 (7x^2+6x-2)

Explanation:

we shall use the product rule here.

the derivative of (x+1) is 1.

the derivative of (x^2-2)^3 is 2x × 3 × (x^2-2)^2 = 6x(x^2-2)^2

now, use the product rule.

f'(x)=(x^2-2)^3+6x(x+1)(x^2-2)^2

and further simplify to

f'(x)=(x^2-2)^2(6x^2+6x+x^2-2)

-> (x^2-2)^2 (7x^2+6x-2)