Solve 3z^25*5z^8

$$3 z ^ { 25 } \cdot 5 z ^ { 8 }$$

Evaluate

$$15z^{33}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 25 and 8 to get 33.

$$3z^{33}\times 5$$

Multiply 3 and 5 to get 15.

$$15z^{33}$$

Differentiate w.r.t. z

$$495z^{32}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 25 and 8 to get 33.

$$\frac{\mathrm{d}}{\mathrm{d}z}(3z^{33}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}z}(15z^{33})$$

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

$$33\times 15z^{33-1}$$

Multiply 33 times 15.

$$495z^{33-1}$$

Subtract 1 from 33.

$$495z^{32}$$