Solve yz^3divyz^6=

$$y z ^ { 3 } \div y z ^ { 6 } =$$

Evaluate

$$z^{9}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$z^{3}z^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$z^{9}$$

Differentiate w.r.t. z

$$9z^{8}$$

Steps Using Definition of a Derivative

Cancel out y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{3}z^{6})$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

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

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

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

Subtract 1 from 9.

$$9z^{8}$$