Solve g(x)=x^4-9x^2+4x+13

$$g ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 4 x + 13$$

Differentiate w.r.t. x

$$4x^{3}-18x+4$$

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}.

$$4x^{4-1}+2\left(-9\right)x^{2-1}+4x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+2\left(-9\right)x^{2-1}+4x^{1-1}$$

Multiply 2 times -9.

$$4x^{3}-18x^{2-1}+4x^{1-1}$$

Subtract 1 from 2.

$$4x^{3}-18x^{1}+4x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-18x^{1}+4x^{0}$$

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

$$4x^{3}-18x+4x^{0}$$

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

$$4x^{3}-18x+4\times 1$$

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

$$4x^{3}-18x+4$$

Evaluate

$$x^{4}-9x^{2}+4x+13$$