Solve 10-x^2-5x^4-2x

$$10- { x }^{ 2 } -5 { x }^{ 4 } -2x$$

Differentiate w.r.t. x

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

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}.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Multiply 4 times -5.

$$-2x^{1}-20x^{4-1}-2x^{1-1}$$

Subtract 1 from 4.

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

Subtract 1 from 1.

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

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

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

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

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

Evaluate

$$10-2x-x^{2}-5x^{4}$$