Solve -5z^4(3z^5)

$$- 5 z ^ { 4 } ( 3 z ^ { 5 } )$$

Evaluate

$$-15z^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$-5z^{9}\times 3$$

Multiply -5 and 3 to get -15.

$$-15z^{9}$$

Differentiate w.r.t. z

$$-135z^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-5z^{9}\times 3)$$

Multiply -5 and 3 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-15z^{9})$$

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

$$9\left(-15\right)z^{9-1}$$

Multiply 9 times -15.

$$-135z^{9-1}$$

Subtract 1 from 9.

$$-135z^{8}$$