Solve frac{sqrt[3]{k}sqrt[5]{k^4}}{k^-2}

$$\frac{ \sqrt[ 3 ]{ k } \sqrt[ 5 ]{ { k }^{ 4 } } }{ { k }^{ -2 } }$$

Differentiate w.r.t. k

$$\frac{47k^{\frac{32}{15}}}{15}$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{\sqrt[3]{k}\sqrt[5]{k^{4}}}{k^{-2}}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{\sqrt[3]{k}\sqrt[5]{k^{4}}}{k^{-2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\sqrt[5]{k^{4}}k^{\frac{7}{3}})$$

Expand the expression.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{\frac{47}{15}})$$

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

$$\frac{47}{15}k^{\frac{47}{15}-1}$$

Subtract 1 from \frac{47}{15}.

$$\frac{47}{15}k^{\frac{32}{15}}$$

Evaluate

$$k^{\frac{47}{15}}$$