What is the derivative of 4 / (x+3)?

Nov 1, 2016

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

Explanation:

This problem can be solved with the use of the chain rule...

$y = 4 {\left(x + 3\right)}^{- 1}$

$y = 4 {u}^{- 1}$

$\frac{\mathrm{dy}}{\mathrm{du}} = - 4 {u}^{- 2} = - \frac{4}{{u}^{2}} = - \frac{4}{x + 3} ^ 2$

$u = x + 3$

$\frac{\mathrm{du}}{\mathrm{dx}} = 1$

$\frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}} = - \frac{4}{x + 3} ^ 2 = \frac{\mathrm{dy}}{\mathrm{dx}}$