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1/x-3/x^3
The derivative of the function/ 1/x-3/x^3

Derivative of 1/x-3/x^3

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
1   3 
- - --
x    3
    x
−3x3+1x- \frac{3}{x^{3}} + \frac{1}{x} 
1/x - 3/x^3
Detail solution

  1. Differentiate −3x3+1x- \frac{3}{x^{3}} + \frac{1}{x} term by term:

    1. Apply the power rule: 1x\frac{1}{x} goes to −1x2- \frac{1}{x^{2}}

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

      1. Let u=x3u = x^{3}.

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

      3. Then, apply the chain rule. Multiply by ddxx3\frac{d}{d x} x^{3}:

        1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

        The result of the chain rule is:

        −3x4- \frac{3}{x^{4}}

      So, the result is: 9x4\frac{9}{x^{4}}

    The result is: −1x2+9x4- \frac{1}{x^{2}} + \frac{9}{x^{4}}

  2. Now simplify:

    9−x2x4\frac{9 - x^{2}}{x^{4}}

The answer is:

9−x2x4\frac{9 - x^{2}}{x^{4}}

The graph
02468-8-6-4-2-1010-100000100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1    9 
- -- + --
   2    4
  x    x
−1x2+9x4- \frac{1}{x^{2}} + \frac{9}{x^{4}}
Simplify
The second derivative [src] 
  /    18\
2*|1 - --|
  |     2|
  \    x /
----------
     3    
    x
2(1−18x2)x3\frac{2 \left(1 - \frac{18}{x^{2}}\right)}{x^{3}}
Simplify
The third derivative [src] 
  /     30\
6*|-1 + --|
  |      2|
  \     x /
-----------
      4    
     x
6(−1+30x2)x4\frac{6 \left(-1 + \frac{30}{x^{2}}\right)}{x^{4}}
Simplify
The graph
Derivative of 1/x-3/x^3
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