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sinx/x^2

Derivative of sinx/x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x)
------
   2  
  x   
$$\frac{\sin{\left(x \right)}}{x^{2}}$$
d /sin(x)\
--|------|
dx|   2  |
  \  x   /
$$\frac{d}{d x} \frac{\sin{\left(x \right)}}{x^{2}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of sine is cosine:

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
cos(x)   2*sin(x)
------ - --------
   2         3   
  x         x    
$$\frac{\cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}$$
The second derivative [src]
          4*cos(x)   6*sin(x)
-sin(x) - -------- + --------
             x           2   
                        x    
-----------------------------
               2             
              x              
$$\frac{- \sin{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{x} + \frac{6 \sin{\left(x \right)}}{x^{2}}}{x^{2}}$$
The third derivative [src]
          24*sin(x)   6*sin(x)   18*cos(x)
-cos(x) - --------- + -------- + ---------
               3         x            2   
              x                      x    
------------------------------------------
                     2                    
                    x                     
$$\frac{- \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x} + \frac{18 \cos{\left(x \right)}}{x^{2}} - \frac{24 \sin{\left(x \right)}}{x^{3}}}{x^{2}}$$
The graph
Derivative of sinx/x^2