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1/sqrt(x^2+4)

Derivative of 1/sqrt(x^2+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
       1     
1*-----------
     ________
    /  2     
  \/  x  + 4 
$$1 \cdot \frac{1}{\sqrt{x^{2} + 4}}$$
d /       1     \
--|1*-----------|
dx|     ________|
  |    /  2     |
  \  \/  x  + 4 /
$$\frac{d}{d x} 1 \cdot \frac{1}{\sqrt{x^{2} + 4}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of the constant is zero.

    To find :

    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:

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
        -x          
--------------------
            ________
/ 2    \   /  2     
\x  + 4/*\/  x  + 4 
$$- \frac{x}{\sqrt{x^{2} + 4} \left(x^{2} + 4\right)}$$
The second derivative [src]
         2 
      3*x  
-1 + ------
          2
     4 + x 
-----------
        3/2
/     2\   
\4 + x /   
$$\frac{\frac{3 x^{2}}{x^{2} + 4} - 1}{\left(x^{2} + 4\right)^{\frac{3}{2}}}$$
The third derivative [src]
     /         2 \
     |      5*x  |
-3*x*|-3 + ------|
     |          2|
     \     4 + x /
------------------
           5/2    
   /     2\       
   \4 + x /       
$$- \frac{3 x \left(\frac{5 x^{2}}{x^{2} + 4} - 3\right)}{\left(x^{2} + 4\right)^{\frac{5}{2}}}$$
The graph
Derivative of 1/sqrt(x^2+4)