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(pi*sin(pi*t/6))/2

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Derivative of:
Derivative of (x^2+2x)^2
Derivative of sin(3*x)/(x+1)
Derivative of (pi*sin(pi*t/6))/2
Derivative of bx^2
Identical expressions
(pi*sin(pi*t/ six))/ two
( Pi multiply by sinus of ( Pi multiply by t divide by 6)) divide by 2
( Pi multiply by sinus of ( Pi multiply by t divide by six)) divide by two
(pisin(pit/6))/2
pisinpit/6/2
(pi*sin(pi*t divide by 6)) divide by 2

The derivative of the function/ (pi*sin(pi*t/6))/2

Derivative of (pisin(pit/6))/2

The solution

You have entered [src]

      /pi*t\
pi*sin|----|
      \ 6  /
------------
     2

$$\frac{\pi \sin{\left(\frac{\pi t}{6} \right)}}{2}$$

(pi*sin((pi*t)/6))/2

Detail solution

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 $u = \frac{\pi t}{6}$ .
  2. The derivative of sine is cosine:
    
    $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d t} \frac{\pi t}{6}$ :
    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.
        
        Apply the power rule: $t$ goes to $1$
        
        So, the result is: $\pi$
      So, the result is: $\frac{\pi}{6}$
    The result of the chain rule is:
    
    $\frac{\pi \cos{\left(\frac{\pi t}{6} \right)}}{6}$
  So, the result is: $\frac{\pi^{2} \cos{\left(\frac{\pi t}{6} \right)}}{6}$
So, the result is: $\frac{\pi^{2} \cos{\left(\frac{\pi t}{6} \right)}}{12}$
Now simplify:

$\frac{\pi^{2} \cos{\left(\frac{\pi t}{6} \right)}}{12}$

The answer is:

$\frac{\pi^{2} \cos{\left(\frac{\pi t}{6} \right)}}{12}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2    /pi*t\
pi *cos|----|
       \ 6  /
-------------
      12

$$\frac{\pi^{2} \cos{\left(\frac{\pi t}{6} \right)}}{12}$$

Simplify

The second derivative [src]

   3    /pi*t\ 
-pi *sin|----| 
        \ 6  / 
---------------
       72

$$- \frac{\pi^{3} \sin{\left(\frac{\pi t}{6} \right)}}{72}$$

Simplify

The third derivative [src]

   4    /pi*t\ 
-pi *cos|----| 
        \ 6  / 
---------------
      432

$$- \frac{\pi^{4} \cos{\left(\frac{\pi t}{6} \right)}}{432}$$

Simplify

The graph

Derivative of (pi*sin(pi*t/6))/2