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sqrt(x^2+4)
The derivative of the function/ sqrt(x^2+4)

Derivative of sqrt(x^2+4)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   ________
  /  2     
\/  x  + 4
x2+4\sqrt{x^{2} + 4} 
sqrt(x^2 + 4)
Detail solution

  1. Let u=x2+4u = x^{2} + 4.

  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+4)\frac{d}{d x} \left(x^{2} + 4\right):

    1. Differentiate x2+4x^{2} + 4 term by term:

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

      2. The derivative of the constant 44 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    xx2+4\frac{x}{\sqrt{x^{2} + 4}}

  4. Now simplify:

    xx2+4\frac{x}{\sqrt{x^{2} + 4}}

The answer is:

xx2+4\frac{x}{\sqrt{x^{2} + 4}}

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     
\/  x  + 4
xx2+4\frac{x}{\sqrt{x^{2} + 4}}
Simplify
The second derivative [src] 
        2  
       x   
 1 - ------
          2
     4 + x 
-----------
   ________
  /      2 
\/  4 + x
−x2x2+4+1x2+4\frac{- \frac{x^{2}}{x^{2} + 4} + 1}{\sqrt{x^{2} + 4}}
Simplify
The third derivative [src] 
    /        2  \
    |       x   |
3*x*|-1 + ------|
    |          2|
    \     4 + x /
-----------------
           3/2   
   /     2\      
   \4 + x /
3x(x2x2+4−1)(x2+4)32\frac{3 x \left(\frac{x^{2}}{x^{2} + 4} - 1\right)}{\left(x^{2} + 4\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(x^2+4)
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