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(x^2+36)/x

Derivative of (x^2+36)/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2     
x  + 36
-------
   x   
$$\frac{x^{2} + 36}{x}$$
(x^2 + 36)/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

      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     
    x  + 36
2 - -------
        2  
       x   
$$2 - \frac{x^{2} + 36}{x^{2}}$$
The second derivative [src]
  /           2\
  |     36 + x |
2*|-1 + -------|
  |         2  |
  \        x   /
----------------
       x        
$$\frac{2 \left(-1 + \frac{x^{2} + 36}{x^{2}}\right)}{x}$$
The third derivative [src]
  /          2\
  |    36 + x |
6*|1 - -------|
  |        2  |
  \       x   /
---------------
        2      
       x       
$$\frac{6 \left(1 - \frac{x^{2} + 36}{x^{2}}\right)}{x^{2}}$$
The graph
Derivative of (x^2+36)/x