Solve d/dxleft(x^4-5+x^-2+4x^-4right)

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

Evaluate

$$4x^{3}-\frac{2}{x^{3}}-\frac{16}{x^{5}}$$

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}.

$$4x^{4-1}-2x^{-2-1}-4\times 4x^{-4-1}$$

Subtract 1 from 4.

$$4x^{3}-2x^{-2-1}-4\times 4x^{-4-1}$$

Subtract 1 from -2.

$$4x^{3}-2x^{-3}-4\times 4x^{-4-1}$$

Multiply -2 times 1.

$$4x^{3}-2x^{-3}-16x^{-4-1}$$

Subtract 1 from -4.

$$4x^{3}-2x^{-3}-16x^{-5}$$

Differentiate w.r.t. x

$$12x^{2}+\frac{6}{x^{4}}+\frac{80}{x^{6}}$$