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The derivative of the function/ ln(-x²+6x-4)

Derivative of ln(-x²+6x-4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   2          \
log\- x  + 6*x - 4/
$$\log{\left(\left(- x^{2} + 6 x\right) - 4 \right)}$$ 
log(-x^2 + 6*x - 4)
Detail solution

  1. Let .

  2. The derivative of is .

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

    1. Differentiate term by term:

      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 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:

      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] 
   6 - 2*x    
--------------
   2          
- x  + 6*x - 4
$$\frac{6 - 2 x}{\left(- x^{2} + 6 x\right) - 4}$$
Simplify
The second derivative [src] 
  /              2 \
  |    2*(-3 + x)  |
2*|1 - ------------|
  |         2      |
  \    4 + x  - 6*x/
--------------------
         2          
    4 + x  - 6*x
$$\frac{2 \left(- \frac{2 \left(x - 3\right)^{2}}{x^{2} - 6 x + 4} + 1\right)}{x^{2} - 6 x + 4}$$
Simplify
The third derivative [src] 
           /               2 \
           |     4*(-3 + x)  |
4*(-3 + x)*|-3 + ------------|
           |          2      |
           \     4 + x  - 6*x/
------------------------------
                     2        
       /     2      \         
       \4 + x  - 6*x/
$$\frac{4 \left(x - 3\right) \left(\frac{4 \left(x - 3\right)^{2}}{x^{2} - 6 x + 4} - 3\right)}{\left(x^{2} - 6 x + 4\right)^{2}}$$
Simplify
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