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Derivative of ln((2x+1)^(1/2))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /  _________\
log\\/ 2*x + 1 /
$$\log{\left(\sqrt{2 x + 1} \right)}$$
log(sqrt(2*x + 1))
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    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:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   1   
-------
2*x + 1
$$\frac{1}{2 x + 1}$$
The second derivative [src]
   -2     
----------
         2
(1 + 2*x) 
$$- \frac{2}{\left(2 x + 1\right)^{2}}$$
The third derivative [src]
    8     
----------
         3
(1 + 2*x) 
$$\frac{8}{\left(2 x + 1\right)^{3}}$$