Solve x(3/2x^frac{2{3}})

$$x ( \frac { 3 } { 2 } x ^ { \frac { 2 } { 3 } } )$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{5}{3}}\times \frac{3}{2})$$

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

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

Multiply \frac{5}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

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

Subtract 1 from \frac{5}{3}.

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and \frac{2}{3} to get \frac{5}{3}.

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