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y=ln^2((x^2)+1)

Derivative of y=ln^2((x^2)+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2/ 2    \
log \x  + 1/
$$\log{\left(x^{2} + 1 \right)}^{2}$$
log(x^2 + 1)^2
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
       / 2    \
4*x*log\x  + 1/
---------------
      2        
     x  + 1    
$$\frac{4 x \log{\left(x^{2} + 1 \right)}}{x^{2} + 1}$$
The second derivative [src]
  /    2       2    /     2\              \
  | 2*x     2*x *log\1 + x /      /     2\|
4*|------ - ---------------- + log\1 + x /|
  |     2             2                   |
  \1 + x         1 + x                    /
-------------------------------------------
                        2                  
                   1 + x                   
$$\frac{4 \left(- \frac{2 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{2 x^{2}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)}\right)}{x^{2} + 1}$$
The third derivative [src]
    /                        2       2    /     2\\
    |         /     2\    6*x     4*x *log\1 + x /|
8*x*|3 - 3*log\1 + x / - ------ + ----------------|
    |                         2             2     |
    \                    1 + x         1 + x      /
---------------------------------------------------
                             2                     
                     /     2\                      
                     \1 + x /                      
$$\frac{8 x \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - 3 \log{\left(x^{2} + 1 \right)} + 3\right)}{\left(x^{2} + 1\right)^{2}}$$
The graph
Derivative of y=ln^2((x^2)+1)