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Derivative of sin^3x*cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3          
sin (x)*cos(x)
$$\sin^{3}{\left(x \right)} \cos{\left(x \right)}$$
sin(x)^3*cos(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    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:

    ; to find :

    1. The derivative of cosine is negative sine:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     4           2       2   
- sin (x) + 3*cos (x)*sin (x)
$$- \sin^{4}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}$$
The second derivative [src]
 /       2            2   \              
-\- 6*cos (x) + 10*sin (x)/*cos(x)*sin(x)
$$- \left(10 \sin^{2}{\left(x \right)} - 6 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
The third derivative [src]
   4           2       2           2    /       2           2   \        2    /   2           2   \
sin (x) - 9*cos (x)*sin (x) - 3*cos (x)*\- 2*cos (x) + 7*sin (x)/ + 9*sin (x)*\sin (x) - 2*cos (x)/
$$9 \left(\sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} - 3 \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} + \sin^{4}{\left(x \right)} - 9 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}$$