Solve (9g^2+9g+1)+(4g+4)

$$( 9 g ^ { 2 } + 9 g + 1 ) + ( 4 g + 4 )$$

Evaluate

$$9g^{2}+13g+5$$

Solution Steps

Combine 9g and 4g to get 13g.

$$9g^{2}+13g+1+4$$

Add 1 and 4 to get 5.

$$9g^{2}+13g+5$$

Differentiate w.r.t. g

$$18g+13$$

Steps Using Derivative Rule for Sum

Combine 9g and 4g to get 13g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(9g^{2}+13g+1+4)$$

Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}g}(9g^{2}+13g+5)$$

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}.

$$2\times 9g^{2-1}+13g^{1-1}$$

Multiply 2 times 9.

$$18g^{2-1}+13g^{1-1}$$

Subtract 1 from 2.

$$18g^{1}+13g^{1-1}$$

Subtract 1 from 1.

$$18g^{1}+13g^{0}$$

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

$$18g+13g^{0}$$

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

$$18g+13\times 1$$

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

$$18g+13$$