# How do you differentiate f(x)=1/(16x+3)^2 using the quotient rule?

$\frac{d}{\mathrm{dx}} \left(\frac{1}{{\left(16 x + 3\right)}^{2}}\right) = \frac{- 32}{{\left(16 x + 3\right)}^{3}}$
$\frac{d}{\mathrm{dx}} \left(\frac{1}{{\left(16 x + 3\right)}^{2}}\right) = \frac{{\left(16 x + 3\right)}^{2} \cdot \frac{d}{\mathrm{dx}} \left(1\right) - \left(1\right) \frac{d}{\mathrm{dx}} \left({\left(16 x + 3\right)}^{2}\right)}{{\left[{\left(16 x + 3\right)}^{2}\right]}^{2}}$
$= \frac{{\left(16 x + 3\right)}^{2} \cdot \left(0\right) - \left(1\right) \left(2 \left(16 x + 3\right) \left(16\right)\right)}{{\left(16 x + 3\right)}^{4}}$
$= \frac{- 32}{{\left(16 x + 3\right)}^{3}}$