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y=sinx/x^5

Derivative of y=sinx/x^5

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x)
------
   5  
  x   
$$\frac{\sin{\left(x \right)}}{x^{5}}$$
sin(x)/x^5
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)   5*sin(x)
------ - --------
   5         6   
  x         x    
$$\frac{\cos{\left(x \right)}}{x^{5}} - \frac{5 \sin{\left(x \right)}}{x^{6}}$$
The second derivative [src]
          10*cos(x)   30*sin(x)
-sin(x) - --------- + ---------
              x            2   
                          x    
-------------------------------
                5              
               x               
$$\frac{- \sin{\left(x \right)} - \frac{10 \cos{\left(x \right)}}{x} + \frac{30 \sin{\left(x \right)}}{x^{2}}}{x^{5}}$$
The third derivative [src]
          210*sin(x)   15*sin(x)   90*cos(x)
-cos(x) - ---------- + --------- + ---------
               3           x            2   
              x                        x    
--------------------------------------------
                      5                     
                     x                      
$$\frac{- \cos{\left(x \right)} + \frac{15 \sin{\left(x \right)}}{x} + \frac{90 \cos{\left(x \right)}}{x^{2}} - \frac{210 \sin{\left(x \right)}}{x^{3}}}{x^{5}}$$
The graph
Derivative of y=sinx/x^5