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x^2sin(1/x)

Derivative of x^2sin(1/x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2    /1\
x *sin|-|
      \x/
$$x^{2} \sin{\left(\frac{1}{x} \right)}$$
x^2*sin(1/x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. The derivative of sine is cosine:

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

      1. Apply the power rule: goes to

      The result of the chain rule is:

    The result is:


The answer is:

The graph
The first derivative [src]
     /1\          /1\
- cos|-| + 2*x*sin|-|
     \x/          \x/
$$2 x \sin{\left(\frac{1}{x} \right)} - \cos{\left(\frac{1}{x} \right)}$$
The second derivative [src]
                         /1\           
                      sin|-|           
                /1\      \x/        /1\
           2*cos|-| - ------   4*cos|-|
     /1\        \x/     x           \x/
2*sin|-| + ----------------- - --------
     \x/           x              x    
$$2 \sin{\left(\frac{1}{x} \right)} + \frac{2 \cos{\left(\frac{1}{x} \right)} - \frac{\sin{\left(\frac{1}{x} \right)}}{x}}{x} - \frac{4 \cos{\left(\frac{1}{x} \right)}}{x}$$
The third derivative [src]
   /1\
cos|-|
   \x/
------
   4  
  x   
$$\frac{\cos{\left(\frac{1}{x} \right)}}{x^{4}}$$
The graph
Derivative of x^2sin(1/x)