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The derivative of the function/ cos(x)/(5x^2)

Derivative of cos(x)/(5x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
cos(x)
------
    2 
 5*x
$$\frac{\cos{\left(x \right)}}{5 x^{2}}$$ 
cos(x)/((5*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. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    Now plug in to the quotient rule:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1            2*cos(x)
- ----*sin(x) - --------
     2               3  
  5*x             5*x
$$- \frac{1}{5 x^{2}} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{5 x^{3}}$$
Simplify
The second derivative [src] 
          4*sin(x)   6*cos(x)
-cos(x) + -------- + --------
             x           2   
                        x    
-----------------------------
                2            
             5*x
$$\frac{- \cos{\left(x \right)} + \frac{4 \sin{\left(x \right)}}{x} + \frac{6 \cos{\left(x \right)}}{x^{2}}}{5 x^{2}}$$
Simplify
The third derivative [src] 
  24*cos(x)   18*sin(x)   6*cos(x)         
- --------- - --------- + -------- + sin(x)
       3           2         x             
      x           x                        
-------------------------------------------
                       2                   
                    5*x
$$\frac{\sin{\left(x \right)} + \frac{6 \cos{\left(x \right)}}{x} - \frac{18 \sin{\left(x \right)}}{x^{2}} - \frac{24 \cos{\left(x \right)}}{x^{3}}}{5 x^{2}}$$
Simplify
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