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The derivative of the function/ (5-(1/x)+5x^-4)

Derivative of (5-(1/x)+5x^-4)

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

You have entered [src] 
    1   5 
5 - - + --
    x    4
        x
(5−1x)+5x4\left(5 - \frac{1}{x}\right) + \frac{5}{x^{4}} 
5 - 1/x + 5/x^4
Detail solution

  1. Differentiate (5−1x)+5x4\left(5 - \frac{1}{x}\right) + \frac{5}{x^{4}} term by term:

    1. Differentiate 5−1x5 - \frac{1}{x} term by term:

      1. The derivative of the constant 55 is zero.

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

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

        So, the result is: 1x2\frac{1}{x^{2}}

      The result is: 1x2\frac{1}{x^{2}}

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

      1. Apply the power rule: 1x4\frac{1}{x^{4}} goes to −4x5- \frac{4}{x^{5}}

      So, the result is: −20x5- \frac{20}{x^{5}}

    The result is: 1x2−20x5\frac{1}{x^{2}} - \frac{20}{x^{5}}

  2. Now simplify:

    x3−20x5\frac{x^{3} - 20}{x^{5}}

The answer is:

x3−20x5\frac{x^{3} - 20}{x^{5}}

The graph
02468-8-6-4-2-1010-50000005000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1    20
-- - --
 2    5
x    x
1x2−20x5\frac{1}{x^{2}} - \frac{20}{x^{5}}
Simplify
The second derivative [src] 
  /     50\
2*|-1 + --|
  |      3|
  \     x /
-----------
      3    
     x
2(−1+50x3)x3\frac{2 \left(-1 + \frac{50}{x^{3}}\right)}{x^{3}}
Simplify
The third derivative [src] 
  /    100\
6*|1 - ---|
  |      3|
  \     x /
-----------
      4    
     x
6(1−100x3)x4\frac{6 \left(1 - \frac{100}{x^{3}}\right)}{x^{4}}
Simplify
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