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ln(x^2+1)
The derivative of the function/ ln(x^2+1)

Derivative of ln(x^2+1)

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

The graph:

from to

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The solution

You have entered [src] 
   / 2    \
log\x  + 1/
log⁡(x2+1)\log{\left(x^{2} + 1 \right)} 
log(x^2 + 1)
Detail solution

  1. Let u=x2+1u = x^{2} + 1.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(x2+1)\frac{d}{d x} \left(x^{2} + 1\right):

    1. Differentiate x2+1x^{2} + 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant 11 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    2xx2+1\frac{2 x}{x^{2} + 1}

  4. Now simplify:

    2xx2+1\frac{2 x}{x^{2} + 1}

The answer is:

2xx2+1\frac{2 x}{x^{2} + 1}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 2*x  
------
 2    
x  + 1
2xx2+1\frac{2 x}{x^{2} + 1}
Simplify
The second derivative [src] 
  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    1 + x /
--------------
         2    
    1 + x
2(−2x2x2+1+1)x2+1\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 1} + 1\right)}{x^{2} + 1}
Simplify
The third derivative [src] 
    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     1 + x /
-----------------
            2    
    /     2\     
    \1 + x /
4x(4x2x2+1−3)(x2+1)2\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}}
Simplify
The graph
Derivative of ln(x^2+1)
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