Question

How do you differentiate `(5-x^2)(x^3-3x+3)`?

Answer 1

Just multiply it out and then use the Power Rule.

`= 5x^3 - 15x + 15 - x^5 + 3x^3 - 3x^2`

`f(x) = - x^5 + 8x^3 - 3x^2 - 15x + 15`

`d/(dx)[f(x)] = -5x^4 + 24x^2 - 6x - 15`