Solve (7s^2+4s+2)+(3s+2-s^2)

$$( 7 s ^ { 2 } + 4 s + 2 ) + ( 3 s + 2 - s ^ { 2 } )$$

Evaluate

$$6s^{2}+7s+4$$

Solution Steps

Combine 4s and 3s to get 7s.

$$7s^{2}+7s+2+2-s^{2}$$

Add 2 and 2 to get 4.

$$7s^{2}+7s+4-s^{2}$$

Combine 7s^{2} and -s^{2} to get 6s^{2}.

$$6s^{2}+7s+4$$

Differentiate w.r.t. s

$$12s+7$$

Steps Using Derivative Rule for Sum

Combine 4s and 3s to get 7s.

$$\frac{\mathrm{d}}{\mathrm{d}s}(7s^{2}+7s+2+2-s^{2})$$

Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}s}(7s^{2}+7s+4-s^{2})$$

Combine 7s^{2} and -s^{2} to get 6s^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(6s^{2}+7s+4)$$

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}.

$$2\times 6s^{2-1}+7s^{1-1}$$

Multiply 2 times 6.

$$12s^{2-1}+7s^{1-1}$$

Subtract 1 from 2.

$$12s^{1}+7s^{1-1}$$

Subtract 1 from 1.

$$12s^{1}+7s^{0}$$

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

$$12s+7s^{0}$$

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

$$12s+7\times 1$$

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

$$12s+7$$