Derivative of 4x^-2

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4 
--
 2
x

$$\frac{4}{x^{2}}$$

4/x^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x^{2}}$ goes to $- \frac{2}{x^{3}}$
So, the result is: $- \frac{8}{x^{3}}$

The answer is:

$- \frac{8}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-8 
---
  3
 x

$$- \frac{8}{x^{3}}$$

Simplify

The second derivative [src]

24
--
 4
x

$$\frac{24}{x^{4}}$$

Simplify

The third derivative [src]

-96 
----
  5 
 x

$$- \frac{96}{x^{5}}$$

Simplify

The graph