Mister Exam

Derivative of (sin(pi*x/2))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /pi*x\
sin|----|
   \ 2  /
$$\sin{\left(\frac{\pi x}{2} \right)}$$
d /   /pi*x\\
--|sin|----||
dx\   \ 2  //
$$\frac{d}{d x} \sin{\left(\frac{\pi x}{2} \right)}$$
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  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. Apply the power rule: goes to

      So, the result is:

    The result of the chain rule is:


The answer is:

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