Find a formula for the derivative of a given function

by RoRi

September 12, 2015

Find a formula for the derivative of the function

$f(x) = x^{-\frac{1}{2}} + x^{-\frac{1}{3}} + x^{-\frac{1}{4}} \qquad x > 0.$

Using the formula for the derivative of a rational power of $x$ , we have

$f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} - \frac{1}{3} x^{-\frac{4}{3}} - \frac{1}{4}x^{-\frac{5}{4}} \qquad x > 0.$

Stumbling Robot