Solve y/14-3y/14

$$\frac { y } { 14 } - \frac { 3 y } { 14 }$$

Evaluate

$$-\frac{y}{7}$$

Short Solution Steps

Since \frac{y}{14} and \frac{3y}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y-3y}{14}$$

Combine like terms in y-3y.

$$\frac{-2y}{14}$$

Divide -2y by 14 to get -\frac{1}{7}y.

$$-\frac{1}{7}y$$

Differentiate w.r.t. y

$$-\frac{1}{7} = -0.14285714285714285$$

Steps Using Definition of a Derivative

Since \frac{y}{14} and \frac{3y}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y-3y}{14})$$

Combine like terms in y-3y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-2y}{14})$$

Divide -2y by 14 to get -\frac{1}{7}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{7}y)$$

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

$$-\frac{1}{7}y^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{7}y^{0}$$

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

$$-\frac{1}{7}$$