Mister Exam

Other calculators


(-1-x^2)/x

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
      2
-1 - x 
-------
   x   
$$\frac{- x^{2} - 1}{x}$$
  /      2\
d |-1 - x |
--|-------|
dx\   x   /
$$\frac{d}{d x} \frac{- x^{2} - 1}{x}$$
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

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