Solve frac{s^-frac{7{15}}}{s^-frac{13{10}}}

$$\frac { s ^ { - \frac { 7 } { 15 } } } { s ^ { - \frac { 13 } { 10 } } }$$

Differentiate w.r.t. s

$$\frac{5}{6\sqrt[6]{s}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{1}s^{-\frac{7}{15}-\left(-\frac{13}{10}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{\frac{5}{6}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{5}{6}s^{\frac{5}{6}-1}$$

Do the arithmetic.

$$\frac{5}{6}s^{-\frac{1}{6}}$$

Evaluate

$$s^{\frac{5}{6}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{13}{10} from -\frac{7}{15} to get \frac{5}{6}.

$$s^{\frac{5}{6}}$$