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Derivative of:
Derivative of x^2+3x
Derivative of x^2-3*x+2
Derivative of (x-2)^2*(x-4)+5
Derivative of (x^2-1)*(x^4+2)
Identical expressions
- one / three *sin(3x)
minus 1 divide by 3 multiply by sinus of (3x)
minus one divide by three multiply by sinus of (3x)
-1/3sin(3x)
-1/3sin3x
-1 divide by 3*sin(3x)
Similar expressions
1/3*sin(3x)
-1/3*sin(3*x)

The derivative of the function/ -1/3*sin(3x)

Derivative of -1/3*sin(3x)

The solution

You have entered [src]

-sin(3*x) 
----------
    3

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

d /-sin(3*x) \
--|----------|
dx\    3     /

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

Transform

Detail solution

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 sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$ :
  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:
  
  $3 \cos{\left(3 x \right)}$
So, the result is: $- \cos{\left(3 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-cos(3*x)

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

Simplify

The second derivative [src]

3*sin(3*x)

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

Simplify

The third derivative [src]

9*cos(3*x)

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

Simplify

The graph

Derivative of -1/3*sin(3x)