Solve xy/2/4y

$$\frac{ \frac{ xy }{ 2 } }{ 4y }$$

Evaluate

$$\frac{x}{8}$$

Solution Steps

Express \frac{\frac{xy}{2}}{4y} as a single fraction.

$$\frac{xy}{2\times 4y}$$

Cancel out y in both numerator and denominator.

$$\frac{x}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{x}{8}$$

Differentiate w.r.t. x

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

Express \frac{\frac{xy}{2}}{4y} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xy}{2\times 4y})$$

Cancel out y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{2\times 4})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{8})$$

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

$$\frac{1}{8}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{8}x^{0}$$

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

$$\frac{1}{8}\times 1$$

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

$$\frac{1}{8}$$