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

Jun 19, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{2 x + 1} ^ 2$

#### Explanation:

Quotient rule states if $f \left(x\right) = \frac{g \left(x\right)}{h \left(x\right)}$

then $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\frac{\mathrm{dg}}{\mathrm{dx}} \times h \left(x\right) - \frac{\mathrm{dh}}{\mathrm{dx}} \times g \left(x\right)}{h \left(x\right)} ^ 2$

As $f \left(x\right) = \frac{x}{2 x + 1}$

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