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

Derivative of ln(x^2-4x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Let .

  2. The derivative of is .

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

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. 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:

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