Solve -5w^4(-2w^3)

$$- 5 w ^ { 4 } ( - 2 w ^ { 3 } )$$

Evaluate

$$10w^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-5w^{7}\left(-2\right)$$

Multiply -5 and -2 to get 10.

$$10w^{7}$$

Differentiate w.r.t. w

$$70w^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-5w^{7}\left(-2\right))$$

Multiply -5 and -2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}w}(10w^{7})$$

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

$$7\times 10w^{7-1}$$

Multiply 7 times 10.

$$70w^{7-1}$$

Subtract 1 from 7.

$$70w^{6}$$