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The derivative of the function/ sqrt(4x^2+1)

Derivative of sqrt(4x^2+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   __________
  /    2     
\/  4*x  + 1
$$\sqrt{4 x^{2} + 1}$$ 
sqrt(4*x^2 + 1)
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      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] 
     4*x     
-------------
   __________
  /    2     
\/  4*x  + 1
$$\frac{4 x}{\sqrt{4 x^{2} + 1}}$$
Simplify
The second derivative [src] 
  /         2  \
  |      4*x   |
4*|1 - --------|
  |           2|
  \    1 + 4*x /
----------------
    __________  
   /        2   
 \/  1 + 4*x
$$\frac{4 \left(- \frac{4 x^{2}}{4 x^{2} + 1} + 1\right)}{\sqrt{4 x^{2} + 1}}$$
Simplify
The third derivative [src] 
     /          2  \
     |       4*x   |
48*x*|-1 + --------|
     |            2|
     \     1 + 4*x /
--------------------
             3/2    
   /       2\       
   \1 + 4*x /
$$\frac{48 x \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right)}{\left(4 x^{2} + 1\right)^{\frac{3}{2}}}$$
Simplify
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