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

Derivative of ln^2(4x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2         
log (4*x + 1)
$$\log{\left(4 x + 1 \right)}^{2}$$ 
d /   2         \
--\log (4*x + 1)/
dx
$$\frac{d}{d x} \log{\left(4 x + 1 \right)}^{2}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. The derivative of is .

    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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
8*log(4*x + 1)
--------------
   4*x + 1
$$\frac{8 \log{\left(4 x + 1 \right)}}{4 x + 1}$$
Simplify
The second derivative [src] 
32*(1 - log(1 + 4*x))
---------------------
               2     
      (1 + 4*x)
$$\frac{32 \cdot \left(1 - \log{\left(4 x + 1 \right)}\right)}{\left(4 x + 1\right)^{2}}$$
Simplify
The third derivative [src] 
128*(-3 + 2*log(1 + 4*x))
-------------------------
                 3       
        (1 + 4*x)
$$\frac{128 \cdot \left(2 \log{\left(4 x + 1 \right)} - 3\right)}{\left(4 x + 1\right)^{3}}$$
Simplify
The graph
Derivative of ln^2(4x+1)
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