Solve xy/x/2

$$x \frac{ \frac{ y }{ x } }{ 2 }$$

Evaluate

$$\frac{y}{2}$$

Solution Steps

Express \frac{\frac{y}{x}}{2} as a single fraction.

$$x\times \frac{y}{x\times 2}$$

Express x\times \frac{y}{x\times 2} as a single fraction.

$$\frac{xy}{x\times 2}$$

Cancel out x in both numerator and denominator.

$$\frac{y}{2}$$

Differentiate w.r.t. y

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Express \frac{\frac{y}{x}}{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(x\times \frac{y}{x\times 2})$$

Express x\times \frac{y}{x\times 2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{xy}{x\times 2})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{2})$$

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

$$\frac{1}{2}y^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}y^{0}$$

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

$$\frac{1}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{2}$$