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Derivative of:
Derivative of 1/x^5
Derivative of x^7*e^x
Derivative of x^5*cos(x)
Derivative of x/3+3/x
Integral of d{x}:
sqrt(1+x^2)
Graphing y =:
sqrt(1+x^2)
Limit of the function:
sqrt(1+x^2)
Identical expressions
sqrt(one +x^ two)
square root of (1 plus x squared )
square root of (one plus x to the power of two)
√(1+x^2)
sqrt(1+x2)
sqrt1+x2
sqrt(1+x²)
sqrt(1+x to the power of 2)
sqrt1+x^2
Similar expressions
x*sqrt(1+x^2)
sqrt(1-x^2)
xarcsinx+(sqrt1+x^2)

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

Derivative of sqrt(1+x^2)

The solution

You have entered [src]

   ________
  /      2 
\/  1 + x

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

sqrt(1 + x^2)

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. 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:

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

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 
\/  1 + x

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

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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Identical expressions

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Derivative of sqrt(1+x^2)

The graph:

Piecewise:

The solution