How do you find the derivative of  2/(5x+1)^2?

Oct 22, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{20}{5 x + 1} ^ 3$

Explanation:

$y = \frac{2}{5 x + 1} ^ 2 = 2 {\left(5 x + 1\right)}^{-} 2$

Let $u = 5 x + 1$,

$\frac{d}{\mathrm{du}} 2 {u}^{-} 2 = - 4 {u}^{-} 3 = - 4 {\left(5 x + 1\right)}^{-} 3$

$\frac{d}{\mathrm{dx}} 5 x + 1 = 5$

Using chain rule, $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$,

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 4 {\left(5 x + 1\right)}^{-} 3 \cdot 5$

$= - 20 {\left(5 x + 1\right)}^{-} 3$

$= - \frac{20}{5 x + 1} ^ 3$