Solve 5z^7*6z

$$5 z ^ { 7 } \cdot 6 z$$

Evaluate

$$30z^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$5z^{8}\times 6$$

Multiply 5 and 6 to get 30.

$$30z^{8}$$

Differentiate w.r.t. z

$$240z^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}z}(5z^{8}\times 6)$$

Multiply 5 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}z}(30z^{8})$$

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

$$8\times 30z^{8-1}$$

Multiply 8 times 30.

$$240z^{8-1}$$

Subtract 1 from 8.

$$240z^{7}$$