Solve (9y^2+y-9)+(9y^2-y-4)=

$$( 9 y ^ { 2 } + y - 9 ) + ( 9 y ^ { 2 } - y - 4 ) =$$

Evaluate

$$18y^{2}-13$$

Solution Steps

Combine 9y^{2} and 9y^{2} to get 18y^{2}.

$$18y^{2}+y-9-y-4$$

Combine y and -y to get 0.

$$18y^{2}-9-4$$

Subtract 4 from -9 to get -13.

$$18y^{2}-13$$

Differentiate w.r.t. y

$$36y$$

Steps Using Derivative Rule for Sum

Combine 9y^{2} and 9y^{2} to get 18y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(18y^{2}+y-9-y-4)$$

Combine y and -y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(18y^{2}-9-4)$$

Subtract 4 from -9 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(18y^{2}-13)$$

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}.

$$2\times 18y^{2-1}$$

Multiply 2 times 18.

$$36y^{2-1}$$

Subtract 1 from 2.

$$36y^{1}$$

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

$$36y$$