Solve 460x^4-5x^2+40x-88

$$460 { x }^{ 4 } -5 { x }^{ 2 } +40x-88$$

Differentiate w.r.t. x

$$1840x^{3}-10x+40$$

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}.

$$4\times 460x^{4-1}+2\left(-5\right)x^{2-1}+40x^{1-1}$$

Multiply 4 times 460.

$$1840x^{4-1}+2\left(-5\right)x^{2-1}+40x^{1-1}$$

Subtract 1 from 4.

$$1840x^{3}+2\left(-5\right)x^{2-1}+40x^{1-1}$$

Multiply 2 times -5.

$$1840x^{3}-10x^{2-1}+40x^{1-1}$$

Subtract 1 from 2.

$$1840x^{3}-10x^{1}+40x^{1-1}$$

Subtract 1 from 1.

$$1840x^{3}-10x^{1}+40x^{0}$$

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

$$1840x^{3}-10x+40x^{0}$$

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

$$1840x^{3}-10x+40\times 1$$

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

$$1840x^{3}-10x+40$$

Evaluate

$$460x^{4}-5x^{2}+40x-88$$