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

Jan 8, 2016

by using the Quotient rule.

Explanation:

 y =( x^2 + 2x + 5 )/(x + 1

applying the Quotient rule as follows gives :

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(x + 1\right) . \frac{d}{\mathrm{dx}} \left({x}^{2} + 2 x + 5\right) - \left({x}^{2} + 2 x + 5\right) . \frac{d}{\mathrm{dx}} \left(x + 1\right)}{x + 1} ^ 2$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(x + 1\right) \left(2 x + 2\right) - \left({x}^{2} + 2 x + 5\right) . 1}{x + 1} ^ 2$

'tidying up ' the numerator gives:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 {x}^{2} + 4 x + 2 - {x}^{2} - 2 x - 5}{x + 1} ^ 2$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{x}^{2} + 2 x - 3}{x + 1} ^ 2$