Solve u^frac{11{7}}divu^frac{3{7}}

$$u ^ { \frac { 11 } { 7 } } \div u ^ { \frac { 3 } { 7 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{u^{\frac{11}{7}}}{u^{\frac{3}{7}}}$$

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

$$u^{\frac{11}{7}-\frac{3}{7}}$$

Subtract \frac{3}{7} from \frac{11}{7} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

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

Differentiate w.r.t. u

$$\frac{8\sqrt[7]{u}}{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{11}{7}-\frac{3}{7}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{8}{7}})$$

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}.

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

Do the arithmetic.

$$\frac{8}{7}\sqrt[7]{u}$$