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(x^2-1)/(x*3+1)

Derivative of (x^2-1)/(x*3+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  2    
 x  - 1
-------
x*3 + 1
$$\frac{x^{2} - 1}{x 3 + 1}$$
  /  2    \
d | x  - 1|
--|-------|
dx\x*3 + 1/
$$\frac{d}{d x} \frac{x^{2} - 1}{x 3 + 1}$$
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. 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:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
    / 2    \          
  3*\x  - 1/     2*x  
- ---------- + -------
           2   x*3 + 1
  (x*3 + 1)           
$$\frac{2 x}{x 3 + 1} - \frac{3 \left(x^{2} - 1\right)}{\left(x 3 + 1\right)^{2}}$$
The second derivative [src]
  /                /      2\\
  |      6*x     9*\-1 + x /|
2*|1 - ------- + -----------|
  |    1 + 3*x             2|
  \               (1 + 3*x) /
-----------------------------
           1 + 3*x           
$$\frac{2 \left(- \frac{6 x}{3 x + 1} + 1 + \frac{9 \left(x^{2} - 1\right)}{\left(3 x + 1\right)^{2}}\right)}{3 x + 1}$$
The third derivative [src]
   /       /      2\          \
   |     9*\-1 + x /     6*x  |
18*|-1 - ----------- + -------|
   |               2   1 + 3*x|
   \      (1 + 3*x)           /
-------------------------------
                    2          
           (1 + 3*x)           
$$\frac{18 \cdot \left(\frac{6 x}{3 x + 1} - 1 - \frac{9 \left(x^{2} - 1\right)}{\left(3 x + 1\right)^{2}}\right)}{\left(3 x + 1\right)^{2}}$$
The graph
Derivative of (x^2-1)/(x*3+1)