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-(3*pi*cos(pi*t/6))/2
The derivative of the function/ -(3*pi*cos(pi*t/6))/2

Derivative of -(3*pi*cos(pi*t/6))/2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
         /pi*t\
-3*pi*cos|----|
         \ 6  /
---------------
       2
$$\frac{\left(-1\right) 3 \pi \cos{\left(\frac{\pi t}{6} \right)}}{2}$$ 
  /         /pi*t\\
  |-3*pi*cos|----||
d |         \ 6  /|
--|---------------|
dt\       2       /
$$\frac{d}{d t} \frac{\left(-1\right) 3 \pi \cos{\left(\frac{\pi t}{6} \right)}}{2}$$
Transform
Detail solution

  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. 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. Apply the power rule: goes to

          So, the result is:

        The result of the chain rule is:

      So, the result is:

    So, the result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  2    /pi*t\
pi *sin|----|
       \ 6  /
-------------
      4
$$\frac{\pi^{2} \sin{\left(\frac{\pi t}{6} \right)}}{4}$$
Simplify
The second derivative [src] 
  3    /pi*t\
pi *cos|----|
       \ 6  /
-------------
      24
$$\frac{\pi^{3} \cos{\left(\frac{\pi t}{6} \right)}}{24}$$
Simplify
The third derivative [src] 
   4    /pi*t\ 
-pi *sin|----| 
        \ 6  / 
---------------
      144
$$- \frac{\pi^{4} \sin{\left(\frac{\pi t}{6} \right)}}{144}$$
Simplify
The graph
Derivative of -(3*pi*cos(pi*t/6))/2
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