Solve -v^4(-5v^4)

$$- v ^ { 4 } ( - 5 v ^ { 4 } )$$

Evaluate

$$5v^{8}$$

Solution Steps

Multiply -1 and -5 to get 5.

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

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

$$5v^{8}$$

Differentiate w.r.t. v

$$40v^{7}$$

Steps Using Definition of a Derivative

Multiply -1 and -5 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}v}(5v^{4}v^{4})$$

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

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

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

$$8\times 5v^{8-1}$$

Multiply 8 times 5.

$$40v^{8-1}$$

Subtract 1 from 8.

$$40v^{7}$$