Question

what is the derivative of x^2(x^2-4)

Answer 1

Do this in either of two ways

Expand the polynomial first:

f = x^4 - 4x^2
f' = 4x^3 - 8x

Or, use the product rule:

f = x^2 (x^2 - 4)
f' = 2x (x^2 - 4) + x^2 (2x)
= 2x^3 - 8x + 2x^3
= 4x^3 - 8x