Mister Exam

Derivative of 2.6sin(0.5x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
      /x\
13*sin|-|
      \2/
---------
    5    
$$\frac{13 \sin{\left(\frac{x}{2} \right)}}{5}$$
13*sin(x/2)/5
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:


The answer is:

The graph
The first derivative [src]
      /x\
13*cos|-|
      \2/
---------
    10   
$$\frac{13 \cos{\left(\frac{x}{2} \right)}}{10}$$
The second derivative [src]
       /x\
-13*sin|-|
       \2/
----------
    20    
$$- \frac{13 \sin{\left(\frac{x}{2} \right)}}{20}$$
The third derivative [src]
       /x\
-13*cos|-|
       \2/
----------
    40    
$$- \frac{13 \cos{\left(\frac{x}{2} \right)}}{40}$$