Solve -12-21x+18x^2-2*4x^3

$$- 12 - 21 x + 18 x ^ { 2 } - 2 \cdot 4 x ^ { 3 }$$

Differentiate w.r.t. x

$$-24x^{2}+36x-21$$

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}.

$$-21x^{1-1}+2\times 18x^{2-1}+3\left(-8\right)x^{3-1}$$

Subtract 1 from 1.

$$-21x^{0}+2\times 18x^{2-1}+3\left(-8\right)x^{3-1}$$

Multiply 2 times 18.

$$-21x^{0}+36x^{2-1}+3\left(-8\right)x^{3-1}$$

Subtract 1 from 2.

$$-21x^{0}+36x^{1}+3\left(-8\right)x^{3-1}$$

Multiply 2 times 18.

$$-21x^{0}+36x^{1}-24x^{3-1}$$

Subtract 1 from 3.

$$-21x^{0}+36x^{1}-24x^{2}$$

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

$$-21x^{0}+36x-24x^{2}$$

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

$$-21+36x-24x^{2}$$

Evaluate

$$-8x^{3}+18x^{2}-21x-12$$

Solution Steps

Multiply 2 and 4 to get 8.

$$-12-21x+18x^{2}-8x^{3}$$