Solve x^3-12x^3-2x^2-4x+4

$${ x }^{ 3 } -12 { x }^{ 3 } -2 { x }^{ 2 } -4x+4$$

Differentiate w.r.t. x

$$-33x^{2}-4x-4$$

Steps Using Derivative Rule for Sum

Combine x^{3} and -12x^{3} to get -11x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-11x^{3}-2x^{2}-4x+4)$$

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}.

$$3\left(-11\right)x^{3-1}+2\left(-2\right)x^{2-1}-4x^{1-1}$$

Multiply 3 times -11.

$$-33x^{3-1}+2\left(-2\right)x^{2-1}-4x^{1-1}$$

Subtract 1 from 3.

$$-33x^{2}+2\left(-2\right)x^{2-1}-4x^{1-1}$$

Multiply 2 times -2.

$$-33x^{2}-4x^{2-1}-4x^{1-1}$$

Subtract 1 from 2.

$$-33x^{2}-4x^{1}-4x^{1-1}$$

Subtract 1 from 1.

$$-33x^{2}-4x^{1}-4x^{0}$$

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

$$-33x^{2}-4x-4x^{0}$$

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

$$-33x^{2}-4x-4$$

Evaluate

$$4-4x-2x^{2}-11x^{3}$$

Solution Steps

Combine x^{3} and -12x^{3} to get -11x^{3}.

$$-11x^{3}-2x^{2}-4x+4$$