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(1+x-4sqrtx)/x

Derivative of (1+x-4sqrtx)/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
            ___
1 + x - 4*\/ x 
---------------
       x       
$$\frac{- 4 \sqrt{x} + \left(x + 1\right)}{x}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

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

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
      2                    
1 - -----                  
      ___               ___
    \/ x    1 + x - 4*\/ x 
--------- - ---------------
    x               2      
                   x       
$$\frac{1 - \frac{2}{\sqrt{x}}}{x} - \frac{- 4 \sqrt{x} + \left(x + 1\right)}{x^{2}}$$
The second derivative [src]
         /      2  \                      
       2*|1 - -----|                      
         |      ___|     /            ___\
 1       \    \/ x /   2*\1 + x - 4*\/ x /
---- - ------------- + -------------------
 5/2          2                  3        
x            x                  x         
$$- \frac{2 \left(1 - \frac{2}{\sqrt{x}}\right)}{x^{2}} + \frac{2 \left(- 4 \sqrt{x} + x + 1\right)}{x^{3}} + \frac{1}{x^{\frac{5}{2}}}$$
The third derivative [src]
  /                                   /      2  \\
  |                                 2*|1 - -----||
  |             /            ___\     |      ___||
  |    3      2*\1 + x - 4*\/ x /     \    \/ x /|
3*|- ------ - ------------------- + -------------|
  |     7/2             4                  3     |
  \  2*x               x                  x      /
$$3 \left(\frac{2 \left(1 - \frac{2}{\sqrt{x}}\right)}{x^{3}} - \frac{2 \left(- 4 \sqrt{x} + x + 1\right)}{x^{4}} - \frac{3}{2 x^{\frac{7}{2}}}\right)$$
The graph
Derivative of (1+x-4sqrtx)/x