Solve d/dxfrac{x^frac{1{3}}}{-2/3}

$$\frac { d } { d x } \frac { x ^ { \frac { 1 } { 3 } } } { - \frac { 2 } { 3 } }$$

Evaluate

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

Steps Using Definition of a Derivative

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{3}\left(-\frac{3}{2}\right)x^{\frac{1}{3}-1}$$

Multiply \frac{1}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

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

Subtract 1 from \frac{1}{3}.

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

Differentiate w.r.t. x

$$\frac{1}{3x^{\frac{5}{3}}}$$