Solve (6s^2-4s+8)+(5s^2-6s)

$$( 6 s ^ { 2 } - 4 s + 8 ) + ( 5 s ^ { 2 } - 6 s )$$

Evaluate

$$11s^{2}-10s+8$$

Solution Steps

Combine 6s^{2} and 5s^{2} to get 11s^{2}.

$$11s^{2}-4s+8-6s$$

Combine -4s and -6s to get -10s.

$$11s^{2}-10s+8$$

Differentiate w.r.t. s

$$22s-10$$

Steps Using Derivative Rule for Sum

Combine 6s^{2} and 5s^{2} to get 11s^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(11s^{2}-4s+8-6s)$$

Combine -4s and -6s to get -10s.

$$\frac{\mathrm{d}}{\mathrm{d}s}(11s^{2}-10s+8)$$

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}.

$$2\times 11s^{2-1}-10s^{1-1}$$

Multiply 2 times 11.

$$22s^{2-1}-10s^{1-1}$$

Subtract 1 from 2.

$$22s^{1}-10s^{1-1}$$

Subtract 1 from 1.

$$22s^{1}-10s^{0}$$

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

$$22s-10s^{0}$$

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

$$22s-10$$