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(1+x^2)^(1/2)

Derivative of (1+x^2)^(1/2)

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

The graph:

from to

Piecewise:

The solution

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

  2. Apply the power rule: goes to

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