Solve 5x^4-3x^2-2x-20

$$5 { x }^{ 4 } -3 { x }^{ 2 } -2x-20$$

Differentiate w.r.t. x

$$20x^{3}-6x-2$$

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}.

$$4\times 5x^{4-1}+2\left(-3\right)x^{2-1}-2x^{1-1}$$

Multiply 4 times 5.

$$20x^{4-1}+2\left(-3\right)x^{2-1}-2x^{1-1}$$

Subtract 1 from 4.

$$20x^{3}+2\left(-3\right)x^{2-1}-2x^{1-1}$$

Multiply 2 times -3.

$$20x^{3}-6x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$20x^{3}-6x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$20x^{3}-6x^{1}-2x^{0}$$

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

$$20x^{3}-6x-2x^{0}$$

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

$$20x^{3}-6x-2$$

Evaluate

$$5x^{4}-3x^{2}-2x-20$$