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Derivative of:
Derivative of e^x^2
Derivative of tanh(x)
Derivative of cos²x
Derivative of (π-2x)³
Identical expressions
seven *sin(x-pi/ six)
7 multiply by sinus of (x minus Pi divide by 6)
seven multiply by sinus of (x minus Pi divide by six)
7sin(x-pi/6)
7sinx-pi/6
7*sin(x-pi divide by 6)
Similar expressions
7*sin(x+pi/6)

The derivative of the function/ 7*sin(x-pi/6)

Derivative of 7*sin(x-pi/6)

The solution

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     /    pi\
7*sin|x - --|
     \    6 /

$$7 \sin{\left(x - \frac{\pi}{6} \right)}$$

7*sin(x - pi/6)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x - \frac{\pi}{6}$ .
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 $\frac{d}{d x} \left(x - \frac{\pi}{6}\right)$ :
  1. Differentiate $x - \frac{\pi}{6}$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $- \frac{\pi}{6}$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $\cos{\left(x - \frac{\pi}{6} \right)}$
So, the result is: $7 \cos{\left(x - \frac{\pi}{6} \right)}$
Now simplify:

$7 \sin{\left(x + \frac{\pi}{3} \right)}$

The answer is:

$7 \sin{\left(x + \frac{\pi}{3} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     /    pi\
7*cos|x - --|
     \    6 /

$$7 \cos{\left(x - \frac{\pi}{6} \right)}$$

Simplify

The second derivative [src]

     /    pi\
7*cos|x + --|
     \    3 /

$$7 \cos{\left(x + \frac{\pi}{3} \right)}$$

Simplify

The third derivative [src]

      /    pi\
-7*sin|x + --|
      \    3 /

$$- 7 \sin{\left(x + \frac{\pi}{3} \right)}$$

Simplify