# What is the derivative of f(x) = (3x+4)/( x^2)?

Feb 22, 2017

$f ' \left(x\right) = - \frac{3 x + 8}{x} ^ 3$

#### Explanation:

dividing each term on the numerator by ${x}^{2}$ gives.

$f \left(x\right) = \frac{3 x}{x} ^ 2 + \frac{4}{x} ^ 2 = \frac{3}{x} + \frac{4}{x} ^ 2 = 3 {x}^{-} 1 + 4 {x}^{-} 2$

differentiate each term using the $\textcolor{b l u e}{\text{power rule}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow f ' \left(x\right) = - 3 {x}^{-} 2 - 8 {x}^{-} 3$

$\textcolor{w h i t e}{\Rightarrow f ' \left(x\right)} = - \frac{3}{x} ^ 2 - \frac{8}{x} ^ 3$

$\textcolor{w h i t e}{\Rightarrow f ' \left(x\right)} = - \frac{3 x + 8}{x} ^ 3$