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

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

Evaluate

$$-4w^{3}$$

Solution Steps

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

$$-2w^{3}\times 2$$

Multiply -2 and 2 to get -4.

$$-4w^{3}$$

Differentiate w.r.t. w

$$-12w^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(-2w^{3}\times 2)$$

Multiply -2 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-4w^{3})$$

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

$$3\left(-4\right)w^{3-1}$$

Multiply 3 times -4.

$$-12w^{3-1}$$

Subtract 1 from 3.

$$-12w^{2}$$