Mister Exam

Derivative of ln(1-x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(1 - x)
$$\log{\left(1 - x \right)}$$
log(1 - x)
Detail solution
  1. Let .

  2. The derivative of is .

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

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