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cos(x)/x^2

Derivative of cos(x)/x^2

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. The derivative of cosine is negative sine:

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