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(x^2+1)/x
The derivative of the function/ (x^2+1)/x

Derivative of (x^2+1)/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2    
x  + 1
------
  x
x2+1x\frac{x^{2} + 1}{x} 
(x^2 + 1)/x
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\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(x)=x2+1f{\left(x \right)} = x^{2} + 1 and g(x)=xg{\left(x \right)} = x.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate x2+1x^{2} + 1 term by term:

      1. The derivative of the constant 11 is zero.

      2. Apply the power rule: x2x^{2} goes to 2x2 x

      The result is: 2x2 x

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    Now plug in to the quotient rule:

    x2−1x2\frac{x^{2} - 1}{x^{2}}

  2. Now simplify:

    1−1x21 - \frac{1}{x^{2}}

The answer is:

1−1x21 - \frac{1}{x^{2}}

The graph
02468-8-6-4-2-1010-100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2    
    x  + 1
2 - ------
       2  
      x
2−x2+1x22 - \frac{x^{2} + 1}{x^{2}}
Simplify
The second derivative [src] 
  /          2\
  |     1 + x |
2*|-1 + ------|
  |        2  |
  \       x   /
---------------
       x
2(−1+x2+1x2)x\frac{2 \left(-1 + \frac{x^{2} + 1}{x^{2}}\right)}{x}
Simplify
The third derivative [src] 
  /         2\
  |    1 + x |
6*|1 - ------|
  |       2  |
  \      x   /
--------------
       2      
      x
6(1−x2+1x2)x2\frac{6 \left(1 - \frac{x^{2} + 1}{x^{2}}\right)}{x^{2}}
Simplify
The graph
Derivative of (x^2+1)/x
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