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

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

Evaluate

$$8w^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-4w^{5}\left(-2\right)$$

Multiply -4 and -2 to get 8.

$$8w^{5}$$

Differentiate w.r.t. w

$$40w^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-4w^{5}\left(-2\right))$$

Multiply -4 and -2 to get 8.

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

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

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

Multiply 5 times 8.

$$40w^{5-1}$$

Subtract 1 from 5.

$$40w^{4}$$