Solve u^2*u*u^-9

$$u ^ { 2 } \cdot u \cdot u ^ { - 9 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$u^{2}u^{1}u^{-9}$$

Use the Multiplication Rule for Exponents.

$$u^{2+1-9}$$

Add the exponents 2 and 1.

$$u^{3-9}$$

Add the exponents 3 and -9.

$$u^{-6}$$

Differentiate w.r.t. u

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{3}u^{-9})$$

To multiply powers of the same base, add their exponents. Add 3 and -9 to get -6.

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

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

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

Subtract 1 from -6.

$$-6u^{-7}$$