Solve (3s^2+3s+3)+(8s^2+6s+9)

$$( 3 s ^ { 2 } + 3 s + 3 ) + ( 8 s ^ { 2 } + 6 s + 9 )$$

Evaluate

$$11s^{2}+9s+12$$

Solution Steps

Combine 3s^{2} and 8s^{2} to get 11s^{2}.

$$11s^{2}+3s+3+6s+9$$

Combine 3s and 6s to get 9s.

$$11s^{2}+9s+3+9$$

Add 3 and 9 to get 12.

$$11s^{2}+9s+12$$

Differentiate w.r.t. s

$$22s+9$$

Steps Using Derivative Rule for Sum

Combine 3s^{2} and 8s^{2} to get 11s^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(11s^{2}+3s+3+6s+9)$$

Combine 3s and 6s to get 9s.

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

Add 3 and 9 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}s}(11s^{2}+9s+12)$$

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}.

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

Multiply 2 times 11.

$$22s^{2-1}+9s^{1-1}$$

Subtract 1 from 2.

$$22s^{1}+9s^{1-1}$$

Subtract 1 from 1.

$$22s^{1}+9s^{0}$$

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

$$22s+9s^{0}$$

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

$$22s+9\times 1$$

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

$$22s+9$$