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ln(x-1)
The derivative of the function/ ln(x-1)

Derivative of ln(x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x - 1)
$$\log{\left(x - 1 \right)}$$ 
log(x - 1)
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 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] 
  1  
-----
x - 1
$$\frac{1}{x - 1}$$
Simplify
The second derivative [src] 
   -1    
---------
        2
(-1 + x)
$$- \frac{1}{\left(x - 1\right)^{2}}$$
Simplify
The third derivative [src] 
    2    
---------
        3
(-1 + x)
$$\frac{2}{\left(x - 1\right)^{3}}$$
Simplify
The graph
Derivative of ln(x-1)
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