Solve u^frac{11{6}}*u^-frac{5{6}}*u^-frac{7{6}}

$$u ^ { \frac { 11 } { 6 } } \cdot u ^ { - \frac { 5 } { 6 } } \cdot u ^ { - \frac { 7 } { 6 } }$$

Evaluate

$$\frac{1}{\sqrt[6]{u}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$u^{\frac{11}{6}}u^{-\frac{5}{6}}u^{-\frac{7}{6}}$$

Use the Multiplication Rule for Exponents.

$$u^{\frac{11-5-7}{6}}$$

Add the exponents \frac{11}{6} and -\frac{5}{6}.

$$u^{1-\frac{7}{6}}$$

Add the exponents 1 and -\frac{7}{6}.

$$u^{-\frac{1}{6}}$$

Differentiate w.r.t. u

$$-\frac{1}{6u^{\frac{7}{6}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{11}{6} and -\frac{5}{6} to get 1.

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

To multiply powers of the same base, add their exponents. Add 1 and -\frac{7}{6} to get -\frac{1}{6}.

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

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{1}{6}u^{-\frac{1}{6}-1}$$

Subtract 1 from -\frac{1}{6}.

$$-\frac{1}{6}u^{-\frac{7}{6}}$$