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4/x^6
The derivative of the function/ 4/x^6

Derivative of 4/x^6

Function f() - derivative -N order at the point
v

The graph:

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The solution

You have entered [src] 
4 
--
 6
x
4x6\frac{4}{x^{6}} 
d /4 \
--|--|
dx| 6|
  \x /
ddx4x6\frac{d}{d x} \frac{4}{x^{6}}
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=x6u = x^{6}.

    2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

    3. Then, apply the chain rule. Multiply by ddxx6\frac{d}{d x} x^{6}:

      1. Apply the power rule: x6x^{6} goes to 6x56 x^{5}

      The result of the chain rule is:

      −6x7- \frac{6}{x^{7}}

    So, the result is: −24x7- \frac{24}{x^{7}}

The answer is:

−24x7- \frac{24}{x^{7}}

The graph
02468-8-6-4-2-1010-500000000500000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-24 
----
  7 
 x
−24x7- \frac{24}{x^{7}}
Simplify
The second derivative [src] 
168
---
  8
 x
168x8\frac{168}{x^{8}}
Simplify
The third derivative [src] 
-1344 
------
   9  
  x
−1344x9- \frac{1344}{x^{9}}
Simplify
The graph
Derivative of 4/x^6
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