Solve 11x^3-12x^2-x+7

$$11 x ^ { 3 } - 12 x ^ { 2 } - x + 7$$

Differentiate w.r.t. x

$$33x^{2}-24x-1$$

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}.

$$3\times 11x^{3-1}+2\left(-12\right)x^{2-1}-x^{1-1}$$

Multiply 3 times 11.

$$33x^{3-1}+2\left(-12\right)x^{2-1}-x^{1-1}$$

Subtract 1 from 3.

$$33x^{2}+2\left(-12\right)x^{2-1}-x^{1-1}$$

Multiply 2 times -12.

$$33x^{2}-24x^{2-1}-x^{1-1}$$

Subtract 1 from 2.

$$33x^{2}-24x^{1}-x^{1-1}$$

Subtract 1 from 1.

$$33x^{2}-24x^{1}-x^{0}$$

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

$$33x^{2}-24x-x^{0}$$

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

$$33x^{2}-24x-1$$

Evaluate

$$11x^{3}-12x^{2}-x+7$$