Mister Exam

Derivative of sin0.5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(0.5*x)
$$\sin{\left(0.5 x \right)}$$
sin(0.5*x)
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  3. Then, apply the chain rule. Multiply by :

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

      1. Apply the power rule: goes to

      So, the result is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
0.5*cos(0.5*x)
$$0.5 \cos{\left(0.5 x \right)}$$
The second derivative [src]
-0.25*sin(0.5*x)
$$- 0.25 \sin{\left(0.5 x \right)}$$
The third derivative [src]
-0.125*cos(0.5*x)
$$- 0.125 \cos{\left(0.5 x \right)}$$