Solve 5y+(y+3y)

$$5 y + ( y + 3 y )$$

Evaluate

$$9y$$

Solution Steps

Combine 5y and y to get 6y.

$$6y+3y$$

Combine 6y and 3y to get 9y.

$$9y$$

Differentiate w.r.t. y

$$9$$

Steps Using Definition of a Derivative

Combine 5y and y to get 6y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y+3y)$$

Combine 6y and 3y to get 9y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(9y)$$

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

$$9y^{1-1}$$

Subtract 1 from 1.

$$9y^{0}$$

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

$$9\times 1$$

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

$$9$$