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Derivative of:
Derivative of 1/3*x^3-4*x
Derivative of x²-4
Derivative of x^((2*e)^(4*x))
Derivative of (x-1)√x^2-2x+2
Graphing y =:
x-ln(1+x^2)
Identical expressions
y=x-ln(one +x^ two)
y equally x minus ln(1 plus x squared )
y equally x minus ln(one plus x to the power of two)
y=x-ln(1+x2)
y=x-ln1+x2
y=x-ln(1+x²)
y=x-ln(1+x to the power of 2)
y=x-ln1+x^2
Similar expressions
y=x+ln(1+x^2)
y=x-ln(1-x^2)

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

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

The solution

You have entered [src]

       /     2\
x - log\1 + x /

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

x - log(1 + x^2)

Detail solution

Differentiate $x - \log{\left(x^{2} + 1 \right)}$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x^{2} + 1$ .
  2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  3. 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:
    
    $\frac{2 x}{x^{2} + 1}$
  So, the result is: $- \frac{2 x}{x^{2} + 1}$
The result is: $- \frac{2 x}{x^{2} + 1} + 1$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

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

The graph

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