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y=sin^3x/2
The derivative of the function/ y=sin^3x/2

Derivative of y=sin^3x/2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3   
sin (x)
-------
   2
$$\frac{\sin^{3}{\left(x \right)}}{2}$$
Transform
Detail solution

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

    1. Let .

    2. Apply the power rule: goes to

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

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    So, the result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2          
3*sin (x)*cos(x)
----------------
       2
$$\frac{3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{2}$$
Simplify
The second derivative [src] 
   /   2           2   \       
-3*\sin (x) - 2*cos (x)/*sin(x)
-------------------------------
               2
$$- \frac{3 \left(\sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}}{2}$$
Simplify
The third derivative [src] 
   /       2           2   \       
-3*\- 2*cos (x) + 7*sin (x)/*cos(x)
-----------------------------------
                 2
$$- \frac{3 \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{2}$$
Simplify
The graph
Derivative of y=sin^3x/2
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