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The derivative of the function/ log(2)sin((2*pi*x+pi)/2)

Derivative of log(2)sin((2*pi*x+pi)/2)

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
          /2*pi*x + pi\
log(2)*sin|-----------|
          \     2     /
$$\log{\left(2 \right)} \sin{\left(\frac{2 \pi x + \pi}{2} \right)}$$ 
log(2)*sin(((2*pi)*x + pi)/2)
Detail solution

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

    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. Differentiate term by term:

          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:

          2. The derivative of the constant is zero.

          The result is:

        So, the result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      /2*pi*x + pi\       
pi*cos|-----------|*log(2)
      \     2     /
$$\pi \log{\left(2 \right)} \cos{\left(\frac{2 \pi x + \pi}{2} \right)}$$
Simplify
The second derivative [src] 
   2                         
-pi *log(2)*sin(pi*(1/2 + x))
$$- \pi^{2} \log{\left(2 \right)} \sin{\left(\pi \left(x + \frac{1}{2}\right) \right)}$$
Simplify
The third derivative [src] 
   3                         
-pi *cos(pi*(1/2 + x))*log(2)
$$- \pi^{3} \log{\left(2 \right)} \cos{\left(\pi \left(x + \frac{1}{2}\right) \right)}$$
Simplify
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