Mister Exam

Derivative of sin(pi*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(pi*x)
$$\sin{\left(\pi x \right)}$$
sin(pi*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]
pi*cos(pi*x)
$$\pi \cos{\left(\pi x \right)}$$
The second derivative [src]
   2          
-pi *sin(pi*x)
$$- \pi^{2} \sin{\left(\pi x \right)}$$
The third derivative [src]
   3          
-pi *cos(pi*x)
$$- \pi^{3} \cos{\left(\pi x \right)}$$
The graph
Derivative of sin(pi*x)