Solve x^4-2x^2-13x-19

$$x ^ { 4 } - 2 x ^ { 2 } - 13 x - 19$$

Differentiate w.r.t. x

$$4x^{3}-4x-13$$

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}.

$$4x^{4-1}+2\left(-2\right)x^{2-1}-13x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+2\left(-2\right)x^{2-1}-13x^{1-1}$$

Multiply 2 times -2.

$$4x^{3}-4x^{2-1}-13x^{1-1}$$

Subtract 1 from 2.

$$4x^{3}-4x^{1}-13x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-4x^{1}-13x^{0}$$

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

$$4x^{3}-4x-13x^{0}$$

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

$$4x^{3}-4x-13$$

Evaluate

$$x^{4}-2x^{2}-13x-19$$