# How do you find the derivative of rational functions: (3/x), (7/x^2), (x^3/sqrt(x))?

Feb 8, 2015

You can use the Quotient Rule or rewrite them as powers, as in:

$\frac{3}{x} = 3 {x}^{-} 1$
Derived: $3 \cdot \left(- 1\right) \cdot {x}^{- 1 - 1} = - 3 {x}^{-} 2 = - \frac{3}{x} ^ 2$

and:

$\frac{7}{x} ^ 2 = 7 {x}^{-} 2$
Derived: $7 \cdot \left(- 2\right) \cdot {x}^{- 2 - 1} = - 14 {x}^{-} 3 = - \frac{14}{x} ^ 3$

and:

${x}^{3} / \sqrt{x} = {x}^{3} \cdot {x}^{- \frac{1}{2}} = {x}^{\frac{5}{2}}$
Derived: $\frac{5}{2} {x}^{\frac{5}{2} - 1} = \frac{5}{2} {x}^{\frac{3}{2}} = \frac{5}{2} x \sqrt{x}$

hope it helps