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Integral of d{x}:
(x^2+1)^(1/2)
Identical expressions
(x^ two + one)^(one / two)
(x squared plus 1) to the power of (1 divide by 2)
(x to the power of two plus one) to the power of (one divide by two)
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(x^2+1)^(1 divide by 2)
Similar expressions
(x^2-1)^(1/2)
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The derivative of the function/ (x^2+1)^(1/2)

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

The solution

You have entered [src]

   ________
  /  2     
\/  x  + 1

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

sqrt(x^2 + 1)

Detail solution

Let $u = x^{2} + 1$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
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. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $1$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} + 1}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x     
-----------
   ________
  /  2     
\/  x  + 1

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

Simplify

The second derivative [src]

        2  
       x   
 1 - ------
          2
     1 + x 
-----------
   ________
  /      2 
\/  1 + x

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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

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Piecewise:

The solution