Solve xy^2/zdivxy/z

$$\frac { x y ^ { 2 } } { z } \div \frac { x y } { z }$$

Evaluate

$$y$$

Solution Steps

Divide \frac{xy^{2}}{z} by \frac{xy}{z} by multiplying \frac{xy^{2}}{z} by the reciprocal of \frac{xy}{z}.

$$\frac{xy^{2}z}{zxy}$$

Cancel out xyz in both numerator and denominator.

$$y$$

Differentiate w.r.t. y

$$1$$

Steps Using Definition of a Derivative

Divide \frac{xy^{2}}{z} by \frac{xy}{z} by multiplying \frac{xy^{2}}{z} by the reciprocal of \frac{xy}{z}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{xy^{2}z}{zxy})$$

Cancel out xyz in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y)$$

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

$$y^{1-1}$$

Subtract 1 from 1.

$$y^{0}$$

For any term t except 0, t^{0}=1.

$$1$$