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y=sinx/x^4
The derivative of the function/ y=sinx/x^4

Derivative of y=sinx/x^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
sin(x)
------
   4  
  x
$$\frac{\sin{\left(x \right)}}{x^{4}}$$ 
d /sin(x)\
--|------|
dx|   4  |
  \  x   /
$$\frac{d}{d x} \frac{\sin{\left(x \right)}}{x^{4}}$$
Transform
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
cos(x)   4*sin(x)
------ - --------
   4         5   
  x         x
$$\frac{\cos{\left(x \right)}}{x^{4}} - \frac{4 \sin{\left(x \right)}}{x^{5}}$$
Simplify
The second derivative [src] 
          8*cos(x)   20*sin(x)
-sin(x) - -------- + ---------
             x            2   
                         x    
------------------------------
               4              
              x
$$\frac{- \sin{\left(x \right)} - \frac{8 \cos{\left(x \right)}}{x} + \frac{20 \sin{\left(x \right)}}{x^{2}}}{x^{4}}$$
Simplify
The third derivative [src] 
          120*sin(x)   12*sin(x)   60*cos(x)
-cos(x) - ---------- + --------- + ---------
               3           x            2   
              x                        x    
--------------------------------------------
                      4                     
                     x
$$\frac{- \cos{\left(x \right)} + \frac{12 \sin{\left(x \right)}}{x} + \frac{60 \cos{\left(x \right)}}{x^{2}} - \frac{120 \sin{\left(x \right)}}{x^{3}}}{x^{4}}$$
Simplify
The graph
Derivative of y=sinx/x^4
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