Solve y-1/3y+y

$$y - \frac { 1 } { 3 } y + y$$

Evaluate

$$\frac{5y}{3}$$

Solution Steps

Combine y and -\frac{1}{3}y to get \frac{2}{3}y.

$$\frac{2}{3}y+y$$

Combine \frac{2}{3}y and y to get \frac{5}{3}y.

$$\frac{5}{3}y$$

Differentiate w.r.t. y

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$

Steps Using Definition of a Derivative

Combine y and -\frac{1}{3}y to get \frac{2}{3}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{3}y+y)$$

Combine \frac{2}{3}y and y to get \frac{5}{3}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5}{3}y)$$

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

$$\frac{5}{3}y^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{3}y^{0}$$

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

$$\frac{5}{3}\times 1$$

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

$$\frac{5}{3}$$