Derivative of cos(x/4)

You have entered [src]

   /x\
cos|-|
   \4/

$$\cos{\left(\frac{x}{4} \right)}$$

d /   /x\\
--|cos|-||
dx\   \4//

$$\frac{d}{d x} \cos{\left(\frac{x}{4} \right)}$$

Transform

Detail solution

Let $u = \frac{x}{4}$ .
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 $\frac{d}{d x} \frac{x}{4}$ :
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: $\frac{1}{4}$
The result of the chain rule is:

$- \frac{\sin{\left(\frac{x}{4} \right)}}{4}$
Now simplify:

$- \frac{\sin{\left(\frac{x}{4} \right)}}{4}$

The answer is:

$- \frac{\sin{\left(\frac{x}{4} \right)}}{4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    /x\ 
-sin|-| 
    \4/ 
--------
   4

$$- \frac{\sin{\left(\frac{x}{4} \right)}}{4}$$

Simplify

The second derivative [src]

    /x\ 
-cos|-| 
    \4/ 
--------
   16

$$- \frac{\cos{\left(\frac{x}{4} \right)}}{16}$$

Simplify

The third derivative [src]

   /x\
sin|-|
   \4/
------
  64

$$\frac{\sin{\left(\frac{x}{4} \right)}}{64}$$

Simplify

The graph