Solve {l}{x^3+2x^2}{+3x+9}

$$\left. \begin{array} { l } { x ^ { 3 } + 2 x ^ { 2 } } \\ { + 3 x + 9 } \end{array} \right.$$

Differentiate w.r.t. x

$$3x^{2}+4x+3$$

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}.

$$3x^{3-1}+2\times 2x^{2-1}+3x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 2x^{2-1}+3x^{1-1}$$

Multiply 2 times 2.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$3x^{2}+4x^{1}+3x^{0}$$

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

$$3x^{2}+4x+3x^{0}$$

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

$$3x^{2}+4x+3\times 1$$

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

$$3x^{2}+4x+3$$

Evaluate

$$x^{3}+2x^{2}+3x+9$$