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Derivative of sin(3*x-pi/12)

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   /      pi\
sin|3*x - --|
   \      12/

$$\sin{\left(3 x - \frac{\pi}{12} \right)}$$

sin(3*x - pi/12)

Detail solution

Let $u = 3 x - \frac{\pi}{12}$ .
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 $\frac{d}{d x} \left(3 x - \frac{\pi}{12}\right)$ :
1. Differentiate $3 x - \frac{\pi}{12}$ 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: $3$
  2. The derivative of the constant $- \frac{\pi}{12}$ is zero.
  The result is: $3$
The result of the chain rule is:

$3 \cos{\left(3 x - \frac{\pi}{12} \right)}$
Now simplify:

$3 \sin{\left(3 x + \frac{5 \pi}{12} \right)}$

The answer is:

$3 \sin{\left(3 x + \frac{5 \pi}{12} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     /      pi\
3*cos|3*x - --|
     \      12/

$$3 \cos{\left(3 x - \frac{\pi}{12} \right)}$$

Simplify

The second derivative [src]

     /      5*pi\
9*cos|3*x + ----|
     \       12 /

$$9 \cos{\left(3 x + \frac{5 \pi}{12} \right)}$$

Simplify

The third derivative [src]

       /      5*pi\
-27*sin|3*x + ----|
       \       12 /

$$- 27 \sin{\left(3 x + \frac{5 \pi}{12} \right)}$$

Simplify

The graph