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sinx-1/2*sin2x

Derivative of sinx-1/2*sin2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         sin(2*x)
sin(x) - --------
            2    
$$\sin{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{2}$$
d /         sin(2*x)\
--|sin(x) - --------|
dx\            2    /
$$\frac{d}{d x} \left(\sin{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{2}\right)$$
Detail solution
  1. Differentiate term by term:

    1. The derivative of sine is cosine:

    2. 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. 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:

        So, the result is:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
-cos(2*x) + cos(x)
$$\cos{\left(x \right)} - \cos{\left(2 x \right)}$$
The second derivative [src]
-sin(x) + 2*sin(2*x)
$$- \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}$$
The third derivative [src]
-cos(x) + 4*cos(2*x)
$$- \cos{\left(x \right)} + 4 \cos{\left(2 x \right)}$$
The graph
Derivative of sinx-1/2*sin2x