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Derivative of:
Derivative of x^2*cos(x)
Derivative of x^2*e^(-x)
Derivative of sin(sqrt(x))
Derivative of ln(1+x^2)
Graphing y =:
ln(1+x^2)
Integral of d{x}:
ln(1+x^2)
ln(1+x^2)
Identical expressions
ln(one +x^ two)
ln(1 plus x squared )
ln(one plus x to the power of two)
ln(1+x2)
ln1+x2
ln(1+x²)
ln(1+x to the power of 2)
ln1+x^2
Similar expressions
ln(1-x^2)
ln(1+x^2)*ln(1-2x)

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

Derivative of ln(1+x^2)

The solution

You have entered [src]

   /     2\
log\1 + x /

$$\log{\left(x^{2} + 1 \right)}$$

d /   /     2\\
--\log\1 + x //
dx

$$\frac{d}{d x} \log{\left(x^{2} + 1 \right)}$$

Transform

Detail solution

Let $u = x^{2} + 1$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 1\right)$ :
1. Differentiate $x^{2} + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
The result of the chain rule is:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*x  
------
     2
1 + x

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

Simplify

The second derivative [src]

  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    1 + x /
--------------
         2    
    1 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 1} + 1\right)}{x^{2} + 1}$$

Simplify

The third derivative [src]

    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     1 + x /
-----------------
            2    
    /     2\     
    \1 + x /

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}}$$

Simplify

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Derivative of ln(1+x^2)

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Piecewise:

The solution