Mister Exam

Other calculators

z=ln(1-2^x)
The derivative of the function/ z=ln(1-2^x)

Derivative of z=ln(1-2^x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /     x\
log\1 - 2 /
$$\log{\left(1 - 2^{x} \right)}$$ 
log(1 - 2^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.

        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] 
  x        
-2 *log(2) 
-----------
        x  
   1 - 2
$$- \frac{2^{x} \log{\left(2 \right)}}{1 - 2^{x}}$$
Simplify
The second derivative [src] 
           /        x  \
 x    2    |       2   |
2 *log (2)*|1 - -------|
           |          x|
           \    -1 + 2 /
------------------------
              x         
        -1 + 2
$$\frac{2^{x} \left(- \frac{2^{x}}{2^{x} - 1} + 1\right) \log{\left(2 \right)}^{2}}{2^{x} - 1}$$
Simplify
The third derivative [src] 
           /         x         2*x  \
 x    3    |      3*2       2*2     |
2 *log (2)*|1 - ------- + ----------|
           |          x            2|
           |    -1 + 2    /      x\ |
           \              \-1 + 2 / /
-------------------------------------
                     x               
               -1 + 2
$$\frac{2^{x} \left(\frac{2 \cdot 2^{2 x}}{\left(2^{x} - 1\right)^{2}} - \frac{3 \cdot 2^{x}}{2^{x} - 1} + 1\right) \log{\left(2 \right)}^{3}}{2^{x} - 1}$$
Simplify
The graph
Derivative of z=ln(1-2^x)
    © Mister Exam – Calculator