Solve (-4r^5)(2r^8)

$$( - 4 r ^ { 5 } ) ( 2 r ^ { 8 } )$$

Evaluate

$$-8r^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$-4r^{13}\times 2$$

Multiply -4 and 2 to get -8.

$$-8r^{13}$$

Differentiate w.r.t. r

$$-104r^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-4r^{13}\times 2)$$

Multiply -4 and 2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-8r^{13})$$

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

$$13\left(-8\right)r^{13-1}$$

Multiply 13 times -8.

$$-104r^{13-1}$$

Subtract 1 from 13.

$$-104r^{12}$$