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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 /
$$\log{\left(2^{x} + 1 \right)}$$ 
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.

      The result is:

    The result of the chain rule is:

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
$$\frac{2^{x} \log{\left(2 \right)}}{2^{x} + 1}$$
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)
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