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The derivative of the function/ y=-4/x^5(-sinx)

Derivative of y=-4/x^5(-sinx)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
-4           
---*(-sin(x))
  5          
 x
$$- \frac{4}{x^{5}} \left(- \sin{\left(x \right)}\right)$$ 
(-4/x^5)*(-sin(x))
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

      So, the result is:

    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] 
  20*sin(x)   4*cos(x)
- --------- + --------
       6          5   
      x          x
$$\frac{4 \cos{\left(x \right)}}{x^{5}} - \frac{20 \sin{\left(x \right)}}{x^{6}}$$
Simplify
The second derivative [src] 
  /          10*cos(x)   30*sin(x)\
4*|-sin(x) - --------- + ---------|
  |              x            2   |
  \                          x    /
-----------------------------------
                  5                
                 x
$$\frac{4 \left(- \sin{\left(x \right)} - \frac{10 \cos{\left(x \right)}}{x} + \frac{30 \sin{\left(x \right)}}{x^{2}}\right)}{x^{5}}$$
Simplify
The third derivative [src] 
  /          210*sin(x)   15*sin(x)   90*cos(x)\
4*|-cos(x) - ---------- + --------- + ---------|
  |               3           x            2   |
  \              x                        x    /
------------------------------------------------
                        5                       
                       x
$$\frac{4 \left(- \cos{\left(x \right)} + \frac{15 \sin{\left(x \right)}}{x} + \frac{90 \cos{\left(x \right)}}{x^{2}} - \frac{210 \sin{\left(x \right)}}{x^{3}}\right)}{x^{5}}$$
Simplify
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