Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of sin(x)+cos(x)
Derivative of cos(x)^2
Derivative of sin(x^3)
Derivative of log(x)^2
Identical expressions
- three sin(pi*x/ three)-3
minus 3 sinus of ( Pi multiply by x divide by 3) minus 3
minus three sinus of ( Pi multiply by x divide by three) minus 3
-3sin(pix/3)-3
-3sinpix/3-3
-3sin(pi*x divide by 3)-3
Similar expressions
3sin(pi*x/3)-3
-3sin(pi*x/3)+3

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Differentiate $- 3 \sin{\left(\frac{\pi x}{3} \right)} - 3$ term by term:
1. 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.
        
        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: $- \pi \cos{\left(\frac{\pi x}{3} \right)}$
2. The derivative of the constant $-3$ is zero.
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