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Derivative of:
Derivative of x^sqrt(x)
Derivative of log(x+2)
Derivative of ln1
Derivative of e^(sin(x)-2*x^3)
Identical expressions
-(one / three)cos(3x+(pi/ six))
minus (1 divide by 3) co sinus of e of (3x plus ( Pi divide by 6))
minus (one divide by three) co sinus of e of (3x plus ( Pi divide by six))
-1/3cos3x+pi/6
-(1 divide by 3)cos(3x+(pi divide by 6))
Similar expressions
-(1/3)cos(3x-(pi/6))
(1/3)cos(3x+(pi/6))

The derivative of the function/ -(1/3)cos(3x+(pi/6))

Derivative of -(1/3)cos(3x+(pi/6))

The solution

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    /      pi\ 
-cos|3*x + --| 
    \      6 / 
---------------
       3

$$- \frac{\cos{\left(3 x + \frac{\pi}{6} \right)}}{3}$$

-cos(3*x + pi/6)/3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x + \frac{\pi}{6}$ .
2. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + \frac{\pi}{6}\right)$ :
  1. Differentiate $3 x + \frac{\pi}{6}$ 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: $x$ goes to $1$
      So, the result is: $3$
    2. The derivative of the constant $\frac{\pi}{6}$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $- 3 \sin{\left(3 x + \frac{\pi}{6} \right)}$
So, the result is: $\sin{\left(3 x + \frac{\pi}{6} \right)}$
Now simplify:

$\sin{\left(3 x + \frac{\pi}{6} \right)}$

The answer is:

$\sin{\left(3 x + \frac{\pi}{6} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   /      pi\
sin|3*x + --|
   \      6 /

$$\sin{\left(3 x + \frac{\pi}{6} \right)}$$

Simplify

The second derivative [src]

     /      pi\
3*cos|3*x + --|
     \      6 /

$$3 \cos{\left(3 x + \frac{\pi}{6} \right)}$$

Simplify

The third derivative [src]

      /      pi\
-9*sin|3*x + --|
      \      6 /

$$- 9 \sin{\left(3 x + \frac{\pi}{6} \right)}$$

Simplify