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y=sin^3*x:3

Derivative of y=sin^3*x:3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3   
sin (x)
-------
   3   
$$\frac{\sin^{3}{\left(x \right)}}{3}$$
  /   3   \
d |sin (x)|
--|-------|
dx\   3   /
$$\frac{d}{d x} \frac{\sin^{3}{\left(x \right)}}{3}$$
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
The first derivative [src]
   2          
sin (x)*cos(x)
$$\sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
 /   2           2   \       
-\sin (x) - 2*cos (x)/*sin(x)
$$- \left(\sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$
The third derivative [src]
 /       2           2   \       
-\- 2*cos (x) + 7*sin (x)/*cos(x)
$$- \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
The graph
Derivative of y=sin^3*x:3