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

Jun 23, 2015

Just multiply it out and then use the Power Rule.

$= 5 {x}^{3} - 15 x + 15 - {x}^{5} + 3 {x}^{3} - 3 {x}^{2}$

$f \left(x\right) = - {x}^{5} + 8 {x}^{3} - 3 {x}^{2} - 15 x + 15$

$\frac{d}{\mathrm{dx}} \left[f \left(x\right)\right] = - 5 {x}^{4} + 24 {x}^{2} - 6 x - 15$