# How do you use the Quotient Rule to prove the Reciprocal Rule?

##### 1 Answer
Mar 30, 2015

$\frac{d}{\mathrm{dx}} \left(f \frac{x}{g} \left(x\right)\right) = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$

and $\frac{d}{\mathrm{dx}} \left(1\right) = 0$

$\frac{d}{\mathrm{dx}} \left(\frac{1}{g} \left(x\right)\right) = \frac{0 \cdot g \left(x\right) - 1 \cdot g ' \left(x\right)}{g \left(x\right)} ^ 2 = \frac{- g ' \left(x\right)}{g \left(x\right)} ^ 2$