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sqrt(x^2+5)
The derivative of the function/ sqrt(x^2+5)

Derivative of sqrt(x^2+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /  2     
\/  x  + 5
$$\sqrt{x^{2} + 5}$$ 
  /   ________\
d |  /  2     |
--\\/  x  + 5 /
dx
$$\frac{d}{d x} \sqrt{x^{2} + 5}$$
Transform
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. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x     
-----------
   ________
  /  2     
\/  x  + 5
$$\frac{x}{\sqrt{x^{2} + 5}}$$
Simplify
The second derivative [src] 
        2  
       x   
 1 - ------
          2
     5 + x 
-----------
   ________
  /      2 
\/  5 + x
$$\frac{- \frac{x^{2}}{x^{2} + 5} + 1}{\sqrt{x^{2} + 5}}$$
Simplify
The third derivative [src] 
    /        2  \
    |       x   |
3*x*|-1 + ------|
    |          2|
    \     5 + x /
-----------------
           3/2   
   /     2\      
   \5 + x /
$$\frac{3 x \left(\frac{x^{2}}{x^{2} + 5} - 1\right)}{\left(x^{2} + 5\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(x^2+5)
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