Solve 02y+3y-1/5y

$$02y+3y- \frac{ 1 }{ 5 } y$$

Evaluate

$$\frac{14y}{5}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$0y+3y-\frac{1}{5}y$$

Anything times zero gives zero.

$$0+3y-\frac{1}{5}y$$

Combine 3y and -\frac{1}{5}y to get \frac{14}{5}y.

$$0+\frac{14}{5}y$$

Anything plus zero gives itself.

$$\frac{14}{5}y$$

Differentiate w.r.t. y

$$\frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps Using Definition of a Derivative

Multiply 0 and 2 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0y+3y-\frac{1}{5}y)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0+3y-\frac{1}{5}y)$$

Combine 3y and -\frac{1}{5}y to get \frac{14}{5}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0+\frac{14}{5}y)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14}{5}y)$$

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

$$\frac{14}{5}y^{1-1}$$

Subtract 1 from 1.

$$\frac{14}{5}y^{0}$$

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

$$\frac{14}{5}\times 1$$

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

$$\frac{14}{5}$$