Solve +1/4ydy

$$+ \frac { 1 } { 4 y } d y$$

Evaluate

$$\frac{d}{4}$$

Solution Steps

Express \frac{1}{4y}d as a single fraction.

$$\frac{d}{4y}y$$

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

$$\frac{dy}{4y}$$

Cancel out y in both numerator and denominator.

$$\frac{d}{4}$$

Differentiate w.r.t. d

$$\frac{1}{4} = 0.25$$

Steps Using Definition of a Derivative

Express \frac{1}{4y}d as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{4y}y)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{dy}{4y})$$

Cancel out y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{4})$$

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

$$\frac{1}{4}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4}d^{0}$$

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

$$\frac{1}{4}\times 1$$

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

$$\frac{1}{4}$$