Solve frac{u^frac{1{2}}}{u^frac{3{8}}}

$$\frac { u ^ { \frac { 1 } { 2 } } } { u ^ { \frac { 3 } { 8 } } }$$

Evaluate

$$\sqrt[8]{u}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\sqrt{u}}{u^{\frac{3}{8}}}$$

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

$$u^{\frac{1}{2}-\frac{3}{8}}$$

Subtract \frac{3}{8} from \frac{1}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt[8]{u}$$

Differentiate w.r.t. u

$$\frac{1}{8u^{\frac{7}{8}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{1}{2}-\frac{3}{8}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt[8]{u})$$

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}.

$$\frac{1}{8}u^{\frac{1}{8}-1}$$

Do the arithmetic.

$$\frac{1}{8}u^{-\frac{7}{8}}$$