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Derivative of:
Derivative of (sin(x))^2
Derivative of x-1
Derivative of sin(x)+cos(x)
Derivative of asin(x)
Identical expressions
- three *sin(pi*x/ three)
minus 3 multiply by sinus of ( Pi multiply by x divide by 3)
minus three multiply by sinus of ( Pi multiply by x divide by three)
-3sin(pix/3)
-3sinpix/3
-3*sin(pi*x divide by 3)
Similar expressions
3*sin(pi*x/3)

The derivative of the function/ -3*sin(pi*x/3)

Derivative of -3sin(pix/3)

The solution

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

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

-3*sin((pi*x)/3)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \frac{\pi x}{3}$ .
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 $\frac{d}{d x} \frac{\pi x}{3}$ :
  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. Apply the power rule: $x$ goes to $1$
      So, the result is: $\pi$
    So, the result is: $\frac{\pi}{3}$
  The result of the chain rule is:
  
  $\frac{\pi \cos{\left(\frac{\pi x}{3} \right)}}{3}$
So, the result is: $- \pi \cos{\left(\frac{\pi x}{3} \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  2    /pi*x\
pi *sin|----|
       \ 3  /
-------------
      3

$$\frac{\pi^{2} \sin{\left(\frac{\pi x}{3} \right)}}{3}$$

Simplify

The third derivative [src]

  3    /pi*x\
pi *cos|----|
       \ 3  /
-------------
      9

$$\frac{\pi^{3} \cos{\left(\frac{\pi x}{3} \right)}}{9}$$

Simplify