Solve (u^2+2u+3)+(8u^2+9u+7)

$$( u ^ { 2 } + 2 u + 3 ) + ( 8 u ^ { 2 } + 9 u + 7 )$$

Evaluate

$$9u^{2}+11u+10$$

Solution Steps

Combine u^{2} and 8u^{2} to get 9u^{2}.

$$9u^{2}+2u+3+9u+7$$

Combine 2u and 9u to get 11u.

$$9u^{2}+11u+3+7$$

Add 3 and 7 to get 10.

$$9u^{2}+11u+10$$

Differentiate w.r.t. u

$$18u+11$$

Steps Using Derivative Rule for Sum

Combine u^{2} and 8u^{2} to get 9u^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(9u^{2}+2u+3+9u+7)$$

Combine 2u and 9u to get 11u.

$$\frac{\mathrm{d}}{\mathrm{d}u}(9u^{2}+11u+3+7)$$

Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}u}(9u^{2}+11u+10)$$

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}.

$$2\times 9u^{2-1}+11u^{1-1}$$

Multiply 2 times 9.

$$18u^{2-1}+11u^{1-1}$$

Subtract 1 from 2.

$$18u^{1}+11u^{1-1}$$

Subtract 1 from 1.

$$18u^{1}+11u^{0}$$

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

$$18u+11u^{0}$$

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

$$18u+11\times 1$$

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

$$18u+11$$