Mister Exam

Derivative of sen(x/2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /x\
sin|-|
   \2/
$$\sin{\left(\frac{x}{2} \right)}$$
sin(x/2)
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:

  4. Now simplify:


The answer is:

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