Solve (2z^5)(5z)

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

Evaluate

$$10z^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$2z^{6}\times 5$$

Multiply 2 and 5 to get 10.

$$10z^{6}$$

Differentiate w.r.t. z

$$60z^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{6}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}z}(10z^{6})$$

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

$$6\times 10z^{6-1}$$

Multiply 6 times 10.

$$60z^{6-1}$$

Subtract 1 from 6.

$$60z^{5}$$