Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x+5)/(x+1)
Derivative of x*2^x
Derivative of e^sin(x)*cos(x)
Derivative of atan(3*x)
Identical expressions
- one /3cos3x+(pi/ six)
minus 1 divide by 3 co sinus of e of 3x plus ( Pi divide by 6)
minus one divide by 3 co sinus of e of 3x plus ( Pi divide by six)
-1/3cos3x+pi/6
-1 divide by 3cos3x+(pi divide by 6)
Similar expressions
1/3cos3x+(pi/6)
-1/3cos3x-(pi/6)
-(1/3)cos(3x+(pi/6))

The derivative of the function/ -1/3cos3x+(pi/6)

Derivative of -1/3cos3x+(pi/6)

The solution

You have entered [src]

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

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

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

Detail solution

Differentiate $- \frac{\cos{\left(3 x \right)}}{3} + \frac{\pi}{6}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 x$ .
  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 $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $- 3 \sin{\left(3 x \right)}$
  So, the result is: $\sin{\left(3 x \right)}$
2. The derivative of the constant $\frac{\pi}{6}$ is zero.
The result is: $\sin{\left(3 x \right)}$

The answer is:

$\sin{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

sin(3*x)

$$\sin{\left(3 x \right)}$$

Simplify

The second derivative [src]

3*cos(3*x)

$$3 \cos{\left(3 x \right)}$$

Simplify

The third derivative [src]

-9*sin(3*x)

$$- 9 \sin{\left(3 x \right)}$$

Simplify