Solve u^frac{11{12}}divu^frac{3{8}}

$$u ^ { \frac { 11 } { 12 } } \div u ^ { \frac { 3 } { 8 } }$$

Evaluate

$$u^{\frac{13}{24}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{u^{\frac{11}{12}}}{u^{\frac{3}{8}}}$$

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

$$u^{\frac{11}{12}-\frac{3}{8}}$$

Subtract \frac{3}{8} from \frac{11}{12} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$u^{\frac{13}{24}}$$

Differentiate w.r.t. u

$$\frac{13}{24u^{\frac{11}{24}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{11}{12}-\frac{3}{8}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{13}{24}})$$

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}.

$$\frac{13}{24}u^{\frac{13}{24}-1}$$

Do the arithmetic.

$$\frac{13}{24}u^{-\frac{11}{24}}$$