Solve frac{u^frac{7{6}}}{u^frac{12{5}}}

$$\frac { u ^ { \frac { 7 } { 6 } } } { u ^ { \frac { 12 } { 5 } } }$$

Evaluate

$$\frac{1}{u^{\frac{37}{30}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{u^{\frac{7}{6}}}{u^{\frac{12}{5}}}$$

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

$$u^{\frac{7}{6}-\frac{12}{5}}$$

Subtract \frac{12}{5} from \frac{7}{6} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$u^{-\frac{37}{30}}$$

Differentiate w.r.t. u

$$-\frac{37}{30u^{\frac{67}{30}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{7}{6}-\frac{12}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{-\frac{37}{30}})$$

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}.

$$-\frac{37}{30}u^{-\frac{37}{30}-1}$$

Do the arithmetic.

$$-\frac{37}{30}u^{-\frac{67}{30}}$$