# How do you use the chain rule to differentiate y=(5x^5-4x^3)^-3?

Apr 30, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 30 x + 36 {x}^{2}}{5 {x}^{2} - 4 {x}^{3}} ^ 4$

#### Explanation:

$y = {\left(5 {x}^{2} - 4 {x}^{3}\right)}^{-} 3$

Differentiate

dy/dx=-3(5x^2-4x^3)^-4* color(green)(d/dx(5x^2-4x^3)color(blue)(rarr "Chain Rule")

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 3 {\left(5 {x}^{2} - 4 {x}^{3}\right)}^{-} 4 \cdot \left(10 x - 12 {x}^{2}\right)$

Simplify

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 30 x + 36 {x}^{2}}{5 {x}^{2} - 4 {x}^{3}} ^ 4$