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(x^2+1)/x^2

Derivative of (x^2+1)/x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2    
x  + 1
------
   2  
  x   
$$\frac{x^{2} + 1}{x^{2}}$$
(x^2 + 1)/x^2
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    \      
  2*\x  + 1/   2*x
- ---------- + ---
       3         2
      x         x 
$$\frac{2 x}{x^{2}} - \frac{2 \left(x^{2} + 1\right)}{x^{3}}$$
The second derivative [src]
  /          2\
  |     1 + x |
6*|-1 + ------|
  |        2  |
  \       x   /
---------------
        2      
       x       
$$\frac{6 \left(-1 + \frac{x^{2} + 1}{x^{2}}\right)}{x^{2}}$$
The third derivative [src]
   /         2\
   |    1 + x |
24*|1 - ------|
   |       2  |
   \      x   /
---------------
        3      
       x       
$$\frac{24 \left(1 - \frac{x^{2} + 1}{x^{2}}\right)}{x^{3}}$$
The graph
Derivative of (x^2+1)/x^2