# How do you find the derivative of (1/(3x^2) - (5/(2x)))?

Nov 21, 2016

$\frac{5}{2 {x}^{2}} - \frac{2}{3 {x}^{3}}$

#### Explanation:

Express the terms of the function in exponent form.

$\Rightarrow \frac{1}{3} {x}^{-} 2 - \frac{5}{2} {x}^{-} 1$

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

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

$\Rightarrow \frac{d}{\mathrm{dx}} \left(\frac{1}{3} {x}^{-} 2 - \frac{5}{2} {x}^{-} 1\right)$

$= - \frac{2}{3} {x}^{-} 3 + \frac{5}{2} {x}^{-} 2 = \frac{5}{2 {x}^{2}} - \frac{2}{3 {x}^{3}}$