Solve -5u^4(-u^4)

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

Evaluate

$$5u^{8}$$

Solution Steps

Multiply -5 and -1 to get 5.

$$5u^{4}u^{4}$$

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

$$5u^{8}$$

Differentiate w.r.t. u

$$40u^{7}$$

Steps Using Definition of a Derivative

Multiply -5 and -1 to get 5.

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

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

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

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

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

Multiply 8 times 5.

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

Subtract 1 from 8.

$$40u^{7}$$