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Derivative of cos(pi*y/(2*b))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /pi*y\
cos|----|
   \2*b /
$$\cos{\left(\frac{\pi y}{2 b} \right)}$$
cos((pi*y)/((2*b)))
Detail solution
  1. Let .

  2. The derivative of cosine is negative sine:

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

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

      1. 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:

      So, the result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The first derivative [src]
       /pi*y\ 
-pi*sin|----| 
       \2*b / 
--------------
     2*b      
$$- \frac{\pi \sin{\left(\frac{\pi y}{2 b} \right)}}{2 b}$$
The second derivative [src]
   2    /pi*y\ 
-pi *cos|----| 
        \2*b / 
---------------
         2     
      4*b      
$$- \frac{\pi^{2} \cos{\left(\frac{\pi y}{2 b} \right)}}{4 b^{2}}$$
4-я производная [src]
  4    /pi*y\
pi *cos|----|
       \2*b /
-------------
        4    
    16*b     
$$\frac{\pi^{4} \cos{\left(\frac{\pi y}{2 b} \right)}}{16 b^{4}}$$
The third derivative [src]
  3    /pi*y\
pi *sin|----|
       \2*b /
-------------
        3    
     8*b     
$$\frac{\pi^{3} \sin{\left(\frac{\pi y}{2 b} \right)}}{8 b^{3}}$$