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Derivative of cos(x)^2*x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2     
cos (x)*x
$$x \cos^{2}{\left(x \right)}$$
cos(x)^2*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 cosine is negative sine:

      The result of the chain rule is:

    ; to find :

    1. Apply the power rule: goes to

    The result is:

  2. Now simplify:


The answer is:

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