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-1/3*sin(3x)

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

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
-sin(3*x) 
----------
    3     
$$- \frac{\sin{\left(3 x \right)}}{3}$$
d /-sin(3*x) \
--|----------|
dx\    3     /
$$\frac{d}{d x} \left(- \frac{\sin{\left(3 x \right)}}{3}\right)$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of sine is cosine:

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
-cos(3*x)
$$- \cos{\left(3 x \right)}$$
The second derivative [src]
3*sin(3*x)
$$3 \sin{\left(3 x \right)}$$
The third derivative [src]
9*cos(3*x)
$$9 \cos{\left(3 x \right)}$$
The graph
Derivative of -1/3*sin(3x)