Solve k^1/7/k^2/7k^-1

$$\frac { k ^ { 1 / 7 } } { k ^ { 2 / 7 } k ^ { - 1 } }$$

Evaluate

$$k^{\frac{6}{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{2}{7} and -1 to get -\frac{5}{7}.

$$\frac{k^{\frac{1}{7}}}{k^{-\frac{5}{7}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{5}{7} from \frac{1}{7} to get \frac{6}{7}.

$$k^{\frac{6}{7}}$$

Differentiate w.r.t. k

$$\frac{6}{7\sqrt[7]{k}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{2}{7} and -1 to get -\frac{5}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{k^{\frac{1}{7}}}{k^{-\frac{5}{7}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{5}{7} from \frac{1}{7} to get \frac{6}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{\frac{6}{7}})$$

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

$$\frac{6}{7}k^{\frac{6}{7}-1}$$

Subtract 1 from \frac{6}{7}.

$$\frac{6}{7}k^{-\frac{1}{7}}$$