Solve 3x^2-11x+6x^3+17

$$3 x ^ { 2 } - 11 x + 6 x ^ { 3 } + 17$$

Differentiate w.r.t. x

$$18x^{2}+6x-11$$

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}.

$$2\times 3x^{2-1}-11x^{1-1}+3\times 6x^{3-1}$$

Multiply 2 times 3.

$$6x^{2-1}-11x^{1-1}+3\times 6x^{3-1}$$

Subtract 1 from 2.

$$6x^{1}-11x^{1-1}+3\times 6x^{3-1}$$

Subtract 1 from 1.

$$6x^{1}-11x^{0}+3\times 6x^{3-1}$$

Multiply 1 times -11.

$$6x^{1}-11x^{0}+18x^{3-1}$$

Subtract 1 from 3.

$$6x^{1}-11x^{0}+18x^{2}$$

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

$$6x-11x^{0}+18x^{2}$$

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

$$6x-11+18x^{2}$$

Evaluate

$$6x^{3}+3x^{2}-11x+17$$