Derivative of 400/x

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400
---
 x

$$\frac{400}{x}$$

400/x

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
So, the result is: $- \frac{400}{x^{2}}$

The answer is:

$- \frac{400}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-400 
-----
   2 
  x

$$- \frac{400}{x^{2}}$$

Simplify

The second derivative [src]

800
---
  3
 x

$$\frac{800}{x^{3}}$$

Simplify

The third derivative [src]

-2400 
------
   4  
  x

$$- \frac{2400}{x^{4}}$$

Simplify

The graph