Solve (3g+9g^4)+(6g-4g^4-2)

$$( 3 g + 9 g ^ { 4 } ) + ( 6 g - 4 g ^ { 4 } - 2 )$$

Evaluate

$$5g^{4}+9g-2$$

Solution Steps

Combine 3g and 6g to get 9g.

$$9g+9g^{4}-4g^{4}-2$$

Combine 9g^{4} and -4g^{4} to get 5g^{4}.

$$9g+5g^{4}-2$$

Differentiate w.r.t. g

$$20g^{3}+9$$

Steps Using Derivative Rule for Sum

Combine 3g and 6g to get 9g.

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

Combine 9g^{4} and -4g^{4} to get 5g^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(9g+5g^{4}-2)$$

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}.

$$9g^{1-1}+4\times 5g^{4-1}$$

Subtract 1 from 1.

$$9g^{0}+4\times 5g^{4-1}$$

Multiply 4 times 5.

$$9g^{0}+20g^{4-1}$$

Subtract 1 from 4.

$$9g^{0}+20g^{3}$$

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

$$9\times 1+20g^{3}$$

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

$$9+20g^{3}$$