Solve f(x)=3x^3-11x^2+11x-7

$$f ( x ) = 3 x ^ { 3 } - 11 x ^ { 2 } + 11 x - 7$$

Differentiate w.r.t. x

$$9x^{2}-22x+11$$

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2\left(-11\right)x^{2-1}+11x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2\left(-11\right)x^{2-1}+11x^{1-1}$$

Multiply 2 times -11.

$$9x^{2}-22x^{2-1}+11x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}-22x^{1}+11x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}-22x^{1}+11x^{0}$$

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

$$9x^{2}-22x+11x^{0}$$

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

$$9x^{2}-22x+11\times 1$$

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

$$9x^{2}-22x+11$$

Evaluate

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