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x^3*cos(x)

Derivative of x^3*cos(x)

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Apply the power rule: goes to

    ; 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]
   3             2       
- x *sin(x) + 3*x *cos(x)
$$- x^{3} \sin{\left(x \right)} + 3 x^{2} \cos{\left(x \right)}$$
The second derivative [src]
  /            2                    \
x*\6*cos(x) - x *cos(x) - 6*x*sin(x)/
$$x \left(- x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right)$$
The third derivative [src]
            3                           2       
6*cos(x) + x *sin(x) - 18*x*sin(x) - 9*x *cos(x)
$$x^{3} \sin{\left(x \right)} - 9 x^{2} \cos{\left(x \right)} - 18 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}$$
The graph
Derivative of x^3*cos(x)