Solve 4g-g^3+3g^2-2

$$4 g - g ^ { 3 } + 3 g ^ { 2 } - 2$$

Differentiate w.r.t. g

$$4+6g-3g^{2}$$

Steps Using Derivative Rule for Sum

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}.

$$4g^{1-1}+3\left(-1\right)g^{3-1}+2\times 3g^{2-1}$$

Subtract 1 from 1.

$$4g^{0}+3\left(-1\right)g^{3-1}+2\times 3g^{2-1}$$

Multiply 3 times -1.

$$4g^{0}-3g^{3-1}+2\times 3g^{2-1}$$

Subtract 1 from 3.

$$4g^{0}-3g^{2}+2\times 3g^{2-1}$$

Multiply 3 times -1.

$$4g^{0}-3g^{2}+6g^{2-1}$$

Subtract 1 from 2.

$$4g^{0}-3g^{2}+6g^{1}$$

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

$$4g^{0}-3g^{2}+6g$$

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

$$4\times 1-3g^{2}+6g$$

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

$$4-3g^{2}+6g$$

Evaluate

$$-g^{3}+3g^{2}+4g-2$$