Solve (3y+4y+4)+(7y-7)

$$( 3 y + 4 y + 4 ) + ( 7 y - 7 )$$

Evaluate

$$14y-3$$

Solution Steps

Combine 3y and 4y to get 7y.

$$7y+4+7y-7$$

Combine 7y and 7y to get 14y.

$$14y+4-7$$

Subtract 7 from 4 to get -3.

$$14y-3$$

Differentiate w.r.t. y

$$14$$

Steps Using Derivative Rule for Sum

Combine 3y and 4y to get 7y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7y+4+7y-7)$$

Combine 7y and 7y to get 14y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(14y+4-7)$$

Subtract 7 from 4 to get -3.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$14y^{1-1}$$

Subtract 1 from 1.

$$14y^{0}$$

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

$$14\times 1$$

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

$$14$$