Solve {r}{-x^4-3x^2-6x}{-8}

$$\left. \begin{array} { r } { - x ^ { 4 } - 3 x ^ { 2 } - 6 x } \\ { - 8 } \end{array} \right.$$

Differentiate w.r.t. x

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

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}.

$$4\left(-1\right)x^{4-1}+2\left(-3\right)x^{2-1}-6x^{1-1}$$

Multiply 4 times -1.

$$-4x^{4-1}+2\left(-3\right)x^{2-1}-6x^{1-1}$$

Subtract 1 from 4.

$$-4x^{3}+2\left(-3\right)x^{2-1}-6x^{1-1}$$

Multiply 2 times -3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-4x^{3}-6x^{1}-6x^{0}$$

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

$$-4x^{3}-6x-6x^{0}$$

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

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

Evaluate

$$-x^{4}-3x^{2}-6x-8$$