Derivative of cost/2

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cos(t)
------
  2

$$\frac{\cos{\left(t \right)}}{2}$$

d /cos(t)\
--|------|
dt\  2   /

$$\frac{d}{d t} \frac{\cos{\left(t \right)}}{2}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of cosine is negative sine:
  
  $\frac{d}{d t} \cos{\left(t \right)} = - \sin{\left(t \right)}$
So, the result is: $- \frac{\sin{\left(t \right)}}{2}$

The answer is:

$- \frac{\sin{\left(t \right)}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-sin(t) 
--------
   2

$$- \frac{\sin{\left(t \right)}}{2}$$

Simplify

The second derivative [src]

-cos(t) 
--------
   2

$$- \frac{\cos{\left(t \right)}}{2}$$

Simplify

The third derivative [src]

sin(t)
------
  2

$$\frac{\sin{\left(t \right)}}{2}$$

Simplify

The graph