Mister Exam

Derivative of sin(0.5*x2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /x2\
sin|--|
   \2 /
$$\sin{\left(\frac{x_{2}}{2} \right)}$$
sin(x2/2)
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:


The answer is:

The graph
The first derivative [src]
   /x2\
cos|--|
   \2 /
-------
   2   
$$\frac{\cos{\left(\frac{x_{2}}{2} \right)}}{2}$$
The second derivative [src]
    /x2\ 
-sin|--| 
    \2 / 
---------
    4    
$$- \frac{\sin{\left(\frac{x_{2}}{2} \right)}}{4}$$
The third derivative [src]
    /x2\ 
-cos|--| 
    \2 / 
---------
    8    
$$- \frac{\cos{\left(\frac{x_{2}}{2} \right)}}{8}$$