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y=log10(e^x+1)
The derivative of the function/ y=log10(e^x+1)

Derivative of y=log10(e^x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   / x    \
log\e  + 1/
-----------
  log(10)
$$\frac{\log{\left(e^{x} + 1 \right)}}{\log{\left(10 \right)}}$$ 
  /   / x    \\
d |log\e  + 1/|
--|-----------|
dx\  log(10)  /
$$\frac{d}{d x} \frac{\log{\left(e^{x} + 1 \right)}}{\log{\left(10 \right)}}$$
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of is .

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

      1. Differentiate term by term:

        1. The derivative of is itself.

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        x       
       e        
----------------
/ x    \        
\e  + 1/*log(10)
$$\frac{e^{x}}{\left(e^{x} + 1\right) \log{\left(10 \right)}}$$
Simplify
The second derivative [src] 
/       x  \    
|      e   |  x 
|1 - ------|*e  
|         x|    
\    1 + e /    
----------------
/     x\        
\1 + e /*log(10)
$$\frac{\left(1 - \frac{e^{x}}{e^{x} + 1}\right) e^{x}}{\left(e^{x} + 1\right) \log{\left(10 \right)}}$$
Simplify
The third derivative [src] 
/        x         2*x \   
|     3*e       2*e    |  x
|1 - ------ + ---------|*e 
|         x           2|   
|    1 + e    /     x\ |   
\             \1 + e / /   
---------------------------
      /     x\             
      \1 + e /*log(10)
$$\frac{\left(1 - \frac{3 e^{x}}{e^{x} + 1} + \frac{2 e^{2 x}}{\left(e^{x} + 1\right)^{2}}\right) e^{x}}{\left(e^{x} + 1\right) \log{\left(10 \right)}}$$
Simplify
The graph
Derivative of y=log10(e^x+1)
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