Solve -x^3+1x^2+2x+3

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

Differentiate w.r.t. x

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

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}.

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

Multiply 3 times -1.

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

Subtract 1 from 3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

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

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

Evaluate

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