Solve f(x)=-x^4-4x^3+6x-6

$$f ( x ) = - x ^ { 4 } - 4 x ^ { 3 } + 6 x - 6$$

Differentiate w.r.t. x

$$6-12x^{2}-4x^{3}$$

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}.

$$4\left(-1\right)x^{4-1}+3\left(-4\right)x^{3-1}+6x^{1-1}$$

Multiply 4 times -1.

$$-4x^{4-1}+3\left(-4\right)x^{3-1}+6x^{1-1}$$

Subtract 1 from 4.

$$-4x^{3}+3\left(-4\right)x^{3-1}+6x^{1-1}$$

Multiply 3 times -4.

$$-4x^{3}-12x^{3-1}+6x^{1-1}$$

Subtract 1 from 3.

$$-4x^{3}-12x^{2}+6x^{1-1}$$

Subtract 1 from 1.

$$-4x^{3}-12x^{2}+6x^{0}$$

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

$$-4x^{3}-12x^{2}+6\times 1$$

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

$$-4x^{3}-12x^{2}+6$$

Evaluate

$$-x^{4}-4x^{3}+6x-6$$