# How do you differentiate f(x) =(1-5x)/(2x^2+7) using the quotient rule?

Jan 11, 2016

f'(x)=(10x^2-4x-35)/((2x^2+7)^2

#### Explanation:

The quotient rule states that :

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

Application to this particular function yields :

$f ' \left(x\right) = \frac{\left(2 {x}^{2} + 7\right) \left(- 5\right) - \left(1 - 5 x\right) \left(4 x\right)}{2 {x}^{2} + 7} ^ 2$

=(10x^2-4x-35)/((2x^2+7)^2.