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Identical expressions
(x^ two + thirty-six)/x
(x squared plus 36) divide by x
(x to the power of two plus thirty minus six) divide by x
(x2+36)/x
x2+36/x
(x²+36)/x
(x to the power of 2+36)/x
x^2+36/x
(x^2+36) divide by x
Similar expressions
(x^2-36)/x

The derivative of the function/ (x^2+36)/x

Derivative of (x^2+36)/x

The solution

You have entered [src]

 2     
x  + 36
-------
   x

$$\frac{x^{2} + 36}{x}$$

(x^2 + 36)/x

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2} + 36$ and $g{\left(x \right)} = x$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} + 36$ term by term:
  1. The derivative of the constant $36$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
Now plug in to the quotient rule:

$\frac{x^{2} - 36}{x^{2}}$
Now simplify:

$1 - \frac{36}{x^{2}}$

The answer is:

$1 - \frac{36}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2     
    x  + 36
2 - -------
        2  
       x

$$2 - \frac{x^{2} + 36}{x^{2}}$$

Simplify

The second derivative [src]

  /           2\
  |     36 + x |
2*|-1 + -------|
  |         2  |
  \        x   /
----------------
       x

$$\frac{2 \left(-1 + \frac{x^{2} + 36}{x^{2}}\right)}{x}$$

Simplify

The third derivative [src]

  /          2\
  |    36 + x |
6*|1 - -------|
  |        2  |
  \       x   /
---------------
        2      
       x

$$\frac{6 \left(1 - \frac{x^{2} + 36}{x^{2}}\right)}{x^{2}}$$

Simplify

The graph

Derivative of (x^2+36)/x