Derivative of 2/3cosx

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2*cos(x)
--------
   3

$$\frac{2 \cos{\left(x \right)}}{3}$$

d /2*cos(x)\
--|--------|
dx\   3    /

$$\frac{d}{d x} \frac{2 \cos{\left(x \right)}}{3}$$

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Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of cosine is negative sine:
  
  $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
So, the result is: $- \frac{2 \sin{\left(x \right)}}{3}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*sin(x)
---------
    3

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

Simplify

The second derivative [src]

-2*cos(x)
---------
    3

$$- \frac{2 \cos{\left(x \right)}}{3}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph