Solve (g^2-4g+11)+(-g^2+8g)

$$( g ^ { 2 } - 4 g + 11 ) + ( - g ^ { 2 } + 8 g )$$

Evaluate

$$4g+11$$

Solution Steps

Combine -4g and 8g to get 4g.

$$g^{2}+4g+11-g^{2}$$

Subtract g^{2} from g^{2} to get 0.

$$4g+11$$

Differentiate w.r.t. g

$$4$$

Steps Using Derivative Rule for Sum

Combine -4g and 8g to get 4g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g^{2}+4g+11-g^{2})$$

Subtract g^{2} from g^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}g}(4g+11)$$

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}.

$$4g^{1-1}$$

Subtract 1 from 1.

$$4g^{0}$$

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

$$4\times 1$$

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

$$4$$