Solve d/dxleft(3/4{x}^frac{2{3}}right)

$$\frac{d}{d x } \left( \frac{ 3 }{ 4 } { x }^{ \frac{ 2 }{ 3 } } \right)$$

Evaluate

$$\frac{1}{2\sqrt[3]{x}}$$

Steps Using Definition of a Derivative

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

$$\frac{2}{3}\times \frac{3}{4}x^{\frac{2}{3}-1}$$

Multiply \frac{2}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

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

Subtract 1 from \frac{2}{3}.

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

Differentiate w.r.t. x

$$-\frac{1}{6x^{\frac{4}{3}}}$$