Solve (15z^5)(-z^2)

$$( 15 z ^ { 5 } ) ( - z ^ { 2 } )$$

Evaluate

$$-15z^{7}$$

Solution Steps

Multiply 15 and -1 to get -15.

$$-15z^{5}z^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-15z^{7}$$

Differentiate w.r.t. z

$$-105z^{6}$$

Steps Using Definition of a Derivative

Multiply 15 and -1 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-15z^{5}z^{2})$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-15z^{7})$$

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

$$7\left(-15\right)z^{7-1}$$

Multiply 7 times -15.

$$-105z^{7-1}$$

Subtract 1 from 7.

$$-105z^{6}$$