Solve (8w^2+2w+6)+(9w^2+5w+7)

$$( 8 w ^ { 2 } + 2 w + 6 ) + ( 9 w ^ { 2 } + 5 w + 7 )$$

Evaluate

$$17w^{2}+7w+13$$

Solution Steps

Combine 8w^{2} and 9w^{2} to get 17w^{2}.

$$17w^{2}+2w+6+5w+7$$

Combine 2w and 5w to get 7w.

$$17w^{2}+7w+6+7$$

Add 6 and 7 to get 13.

$$17w^{2}+7w+13$$

Differentiate w.r.t. w

$$34w+7$$

Steps Using Derivative Rule for Sum

Combine 8w^{2} and 9w^{2} to get 17w^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(17w^{2}+2w+6+5w+7)$$

Combine 2w and 5w to get 7w.

$$\frac{\mathrm{d}}{\mathrm{d}w}(17w^{2}+7w+6+7)$$

Add 6 and 7 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}w}(17w^{2}+7w+13)$$

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}.

$$2\times 17w^{2-1}+7w^{1-1}$$

Multiply 2 times 17.

$$34w^{2-1}+7w^{1-1}$$

Subtract 1 from 2.

$$34w^{1}+7w^{1-1}$$

Subtract 1 from 1.

$$34w^{1}+7w^{0}$$

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

$$34w+7w^{0}$$

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

$$34w+7\times 1$$

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

$$34w+7$$