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The derivative of the function/ -1/2sinx/2

Derivative of -1/2sinx/2

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
/-sin(x) \
|--------|
\   2    /
----------
    2
(−1)12sin⁡(x)2\frac{\left(-1\right) \frac{1}{2} \sin{\left(x \right)}}{2} 
(-sin(x)/2)/2
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

        ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

      So, the result is: −cos⁡(x)2- \frac{\cos{\left(x \right)}}{2}

    So, the result is: −cos⁡(x)4- \frac{\cos{\left(x \right)}}{4}

The answer is:

−cos⁡(x)4- \frac{\cos{\left(x \right)}}{4}

The graph
02468-8-6-4-2-10100.5-0.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-cos(x) 
--------
   4
−cos⁡(x)4- \frac{\cos{\left(x \right)}}{4}
Simplify
The second derivative [src] 
sin(x)
------
  4
sin⁡(x)4\frac{\sin{\left(x \right)}}{4}
Simplify
The third derivative [src] 
cos(x)
------
  4
cos⁡(x)4\frac{\cos{\left(x \right)}}{4}
Simplify
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