Mister Exam

Derivative of ln(1+x²)

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

The graph:

from to

Piecewise:

The solution

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

  2. The derivative of is .

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
 2*x  
------
     2
1 + x 
$$\frac{2 x}{x^{2} + 1}$$
The second derivative [src]
  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    1 + x /
--------------
         2    
    1 + x     
$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 1} + 1\right)}{x^{2} + 1}$$
The third derivative [src]
    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     1 + x /
-----------------
            2    
    /     2\     
    \1 + x /     
$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}}$$
The graph
Derivative of ln(1+x²)