Solve f(x)-2x^2+5x^-4

$$f ( x ) - 2 x ^ { 2 } + 5 x ^ { - 4 }$$

Differentiate w.r.t. x

$$f-4x-\frac{20}{x^{5}}$$

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}.

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

Subtract 1 from 1.

$$fx^{0}+2\left(-2\right)x^{2-1}-4\times 5x^{-4-1}$$

Multiply 2 times -2.

$$fx^{0}-4x^{2-1}-4\times 5x^{-4-1}$$

Subtract 1 from 2.

$$fx^{0}-4x^{1}-4\times 5x^{-4-1}$$

Multiply 2 times -2.

$$fx^{0}-4x^{1}-20x^{-4-1}$$

Subtract 1 from -4.

$$fx^{0}-4x^{1}-20x^{-5}$$

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

$$fx^{0}-4x-20x^{-5}$$

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

$$f\times 1-4x-20x^{-5}$$

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

$$f-4x-20x^{-5}$$

Evaluate

$$fx-2x^{2}+\frac{5}{x^{4}}$$