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The derivative of the function/ (sin*x)/(5*x)

Derivative of (sin*x)/(5*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
sin(x)
------
 5*x
$$\frac{\sin{\left(x \right)}}{5 x}$$ 
sin(x)/((5*x))
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of sine is cosine:

    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           sin(x)
---*cos(x) - ------
5*x              2 
              5*x
$$\frac{1}{5 x} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{5 x^{2}}$$
Simplify
The second derivative [src] 
          2*cos(x)   2*sin(x)
-sin(x) - -------- + --------
             x           2   
                        x    
-----------------------------
             5*x
$$\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{5 x}$$
Simplify
The third derivative [src] 
          6*sin(x)   3*sin(x)   6*cos(x)
-cos(x) - -------- + -------- + --------
              3         x           2   
             x                     x    
----------------------------------------
                  5*x
$$\frac{- \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{6 \cos{\left(x \right)}}{x^{2}} - \frac{6 \sin{\left(x \right)}}{x^{3}}}{5 x}$$
Simplify
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