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

Derivative of sqrt(1+x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /      2 
\/  1 + x
x2+1\sqrt{x^{2} + 1} 
sqrt(1 + x^2)
Detail solution

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

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{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. The derivative of the constant 11 is zero.

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

      The result is: 2x2 x

    The result of the chain rule is:

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

The answer is:

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

The graph
02468-8-6-4-2-101020-10
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x     
-----------
   ________
  /      2 
\/  1 + x
xx2+1\frac{x}{\sqrt{x^{2} + 1}}
Simplify
The second derivative [src] 
        2  
       x   
 1 - ------
          2
     1 + x 
-----------
   ________
  /      2 
\/  1 + x
−x2x2+1+1x2+1\frac{- \frac{x^{2}}{x^{2} + 1} + 1}{\sqrt{x^{2} + 1}}
Simplify
The third derivative [src] 
    /        2  \
    |       x   |
3*x*|-1 + ------|
    |          2|
    \     1 + x /
-----------------
           3/2   
   /     2\      
   \1 + x /
3x(x2x2+1−1)(x2+1)32\frac{3 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(1+x^2)
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