Derivative of cos(x+pi/6)

You have entered [src]

   /    pi\
cos|x + --|
   \    6 /

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

cos(x + pi/6)

Detail solution

Let $u = x + \frac{\pi}{6}$ .
The derivative of cosine is negative sine:

$\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
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:

$- \sin{\left(x + \frac{\pi}{6} \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    /    pi\
-sin|x + --|
    \    6 /

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

Simplify

The second derivative [src]

    /    pi\
-cos|x + --|
    \    6 /

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

Simplify

The third derivative [src]

   /    pi\
sin|x + --|
   \    6 /

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

Simplify