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Derivative of sin(2*x-pi/3)

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   /      pi\
sin|2*x - --|
   \      3 /

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

sin(2*x - pi/3)

Detail solution

Let $u = 2 x - \frac{\pi}{3}$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - \frac{\pi}{3}\right)$ :
1. Differentiate $2 x - \frac{\pi}{3}$ term by term:
  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: $2$
  2. The derivative of the constant $- \frac{\pi}{3}$ is zero.
  The result is: $2$
The result of the chain rule is:

$2 \cos{\left(2 x - \frac{\pi}{3} \right)}$
Now simplify:

$2 \sin{\left(2 x + \frac{\pi}{6} \right)}$

The answer is:

$2 \sin{\left(2 x + \frac{\pi}{6} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     /      pi\
2*cos|2*x - --|
     \      3 /

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

Simplify

The second derivative [src]

     /      pi\
4*cos|2*x + --|
     \      6 /

$$4 \cos{\left(2 x + \frac{\pi}{6} \right)}$$

Simplify

The third derivative [src]

      /      pi\
-8*sin|2*x + --|
      \      6 /

$$- 8 \sin{\left(2 x + \frac{\pi}{6} \right)}$$

Simplify

The graph