Solve v^4v^4v^5

$$v ^ { 4 } v ^ { 4 } v ^ { 5 }$$

Evaluate

$$v^{13}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$v^{4}v^{4}v^{5}$$

Use the Multiplication Rule for Exponents.

$$v^{4+4+5}$$

Add the exponents 4 and 4.

$$v^{8+5}$$

Add the exponents 8 and 5.

$$v^{13}$$

Differentiate w.r.t. v

$$13v^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{8}v^{5})$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{13})$$

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

$$13v^{13-1}$$

Subtract 1 from 13.

$$13v^{12}$$