# How do you find the derivative for f(x) = (3 + 4x) /( 1 + x^2)?

• Quotient rule states that $\left(\frac{a}{b}\right) ' = \frac{a ' b - a b '}{b} ^ 2$
$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{4 \left(1 + {x}^{2}\right) - \left(3 + 4 x\right) \left(2 x\right)}{1 + {x}^{2}} ^ 2$
$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{4 + 4 {x}^{2} - 6 x - 8 {x}^{2}}{1 + {x}^{2}} ^ 2$
$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{- 4 {x}^{2} - 6 x + 4}{1 + {x}^{2}} ^ 2$