Solve 3y-1/2y+y

$$3 y - \frac { 1 } { 2 } y + y$$

Evaluate

$$\frac{7y}{2}$$

Solution Steps

Combine 3y and -\frac{1}{2}y to get \frac{5}{2}y.

$$\frac{5}{2}y+y$$

Combine \frac{5}{2}y and y to get \frac{7}{2}y.

$$\frac{7}{2}y$$

Differentiate w.r.t. y

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps Using Definition of a Derivative

Combine 3y and -\frac{1}{2}y to get \frac{5}{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5}{2}y+y)$$

Combine \frac{5}{2}y and y to get \frac{7}{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7}{2}y)$$

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

$$\frac{7}{2}y^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{2}y^{0}$$

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

$$\frac{7}{2}\times 1$$

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

$$\frac{7}{2}$$