# How do you differentiate f(x) =(1+2x)/(-x^2+1) using the quotient rule?

Dec 29, 2015

The quotient rule states that for $f \left(x\right) = g \frac{x}{h} \left(x\right)$, then $\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h} {\left(x\right)}^{2}$

#### Explanation:

Derivating it following the quotient rule, then:

$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{2 \left(- {x}^{2} + 1\right) - \left(1 + 2 x\right) \left(- 2 x\right)}{- {x}^{2} + 1} ^ 2$

$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{- 2 {x}^{2} + 2 + 2 x + 4 {x}^{2}}{1 - {x}^{2}} ^ 2$

(df(x))/(dx)=(2(x^2+x+1))/((1-x^2)^2