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(x-3)/sqrt(x)
The derivative of the function/ (x-3)/sqrt(x)

Derivative of (x-3)/sqrt(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x - 3
-----
  ___
\/ x
$$\frac{x - 3}{\sqrt{x}}$$ 
d /x - 3\
--|-----|
dx|  ___|
  \\/ x /
$$\frac{d}{d x} \frac{x - 3}{\sqrt{x}}$$
Transform
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

      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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1     x - 3 
----- - ------
  ___      3/2
\/ x    2*x
$$\frac{1}{\sqrt{x}} - \frac{x - 3}{2 x^{\frac{3}{2}}}$$
Simplify
The second derivative [src] 
     3*(-3 + x)
-1 + ----------
        4*x    
---------------
       3/2     
      x
$$\frac{-1 + \frac{3 \left(x - 3\right)}{4 x}}{x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  /    5*(-3 + x)\
3*|6 - ----------|
  \        x     /
------------------
         5/2      
      8*x
$$\frac{3 \cdot \left(6 - \frac{5 \left(x - 3\right)}{x}\right)}{8 x^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of (x-3)/sqrt(x)
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