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y=log(1+cos(x))
The derivative of the function/ y=log(1+cos(x))

Derivative of y=log(1+cos(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(1 + cos(x))
$$\log{\left(\cos{\left(x \right)} + 1 \right)}$$ 
d                  
--(log(1 + cos(x)))
dx
$$\frac{d}{d x} \log{\left(\cos{\left(x \right)} + 1 \right)}$$
Transform
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 cosine is negative sine:

      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] 
 -sin(x)  
----------
1 + cos(x)
$$- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}$$
Simplify
The second derivative [src] 
 /    2              \ 
 | sin (x)           | 
-|---------- + cos(x)| 
 \1 + cos(x)         / 
-----------------------
       1 + cos(x)
$$- \frac{\cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)} + 1}}{\cos{\left(x \right)} + 1}$$
Simplify
The third derivative [src] 
/                        2     \       
|     3*cos(x)      2*sin (x)  |       
|1 - ---------- - -------------|*sin(x)
|    1 + cos(x)               2|       
\                 (1 + cos(x)) /       
---------------------------------------
               1 + cos(x)
$$\frac{\left(1 - \frac{3 \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}$$
Simplify
The graph
Derivative of y=log(1+cos(x))
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