Solve k^3/(k^frac{2{3})(k^-1)}

$$\frac { k ^ { 3 } } { ( k ^ { \frac { 2 } { 3 } } ) ( k ^ { - 1 } ) }$$

Differentiate w.r.t. k

$$\frac{10k^{\frac{7}{3}}}{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{k^{3}}{k^{-\frac{1}{3}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{1}{3} from 3 to get \frac{10}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{\frac{10}{3}})$$

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

$$\frac{10}{3}k^{\frac{10}{3}-1}$$

Subtract 1 from \frac{10}{3}.

$$\frac{10}{3}k^{\frac{7}{3}}$$

Evaluate

$$k^{\frac{10}{3}}$$