Derivative of 4x^-5

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4 
--
 5
x

$$\frac{4}{x^{5}}$$

4/x^5

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x^{5}}$ goes to $- \frac{5}{x^{6}}$
So, the result is: $- \frac{20}{x^{6}}$

The answer is:

$- \frac{20}{x^{6}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-20 
----
  6 
 x

$$- \frac{20}{x^{6}}$$

Simplify

The second derivative [src]

120
---
  7
 x

$$\frac{120}{x^{7}}$$

Simplify

The third derivative [src]

-840 
-----
   8 
  x

$$- \frac{840}{x^{8}}$$

Simplify

The graph