# How do you differentiate f(x)=-x^3*(-5x) using the product rule?

Dec 25, 2015

$20 {x}^{3}$

#### Explanation:

The product rule states that the derivative of a product of two functions is the first function times the derivative of the second, plus the second function times the derivative e of the first.
ie. $\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$.

Application in this particular case yields

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

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

$= 20 {x}^{3}$