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0,5cos(3x-pi/6)
The derivative of the function/ 0,5cos(3x-pi/6)

You entered:

0,5cos(3x-pi/6)

What you mean?

13*cos((3*x - pi)/6)/2
 
13*cos(3*(x - pi)/6)/2
 
13*cos(3*x - pi/6)/2
 
13*cos(3*x - pi/6)/2

Derivative of 0,5cos(3x-pi/6)

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

The graph:

from to

Piecewise:

The solution

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

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of cosine is negative sine:

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        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:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      /      pi\
-3*sin|3*x - --|
      \      6 /
----------------
       2
$$- \frac{3 \sin{\left(3 x - \frac{\pi}{6} \right)}}{2}$$
Simplify
The second derivative [src] 
      /      pi\
-9*sin|3*x + --|
      \      3 /
----------------
       2
$$- \frac{9 \sin{\left(3 x + \frac{\pi}{3} \right)}}{2}$$
Simplify
The third derivative [src] 
       /      pi\
-27*cos|3*x + --|
       \      3 /
-----------------
        2
$$- \frac{27 \cos{\left(3 x + \frac{\pi}{3} \right)}}{2}$$
Simplify
The graph
Derivative of 0,5cos(3x-pi/6)
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