Solve frac{u^frac{3{5}}}{u^frac{3{4}}}

$$\frac { u ^ { \frac { 3 } { 5 } } } { u ^ { \frac { 3 } { 4 } } }$$

Evaluate

$$\frac{1}{u^{\frac{3}{20}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{u^{\frac{3}{5}}}{u^{\frac{3}{4}}}$$

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

$$u^{\frac{3}{5}-\frac{3}{4}}$$

Subtract \frac{3}{4} from \frac{3}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$u^{-\frac{3}{20}}$$

Differentiate w.r.t. u

$$-\frac{3}{20u^{\frac{23}{20}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{3}{5}-\frac{3}{4}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{-\frac{3}{20}})$$

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}.

$$-\frac{3}{20}u^{-\frac{3}{20}-1}$$

Do the arithmetic.

$$-\frac{3}{20}u^{-\frac{23}{20}}$$