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(sin(x)-acot(x))/x^3
The derivative of the function/ (sin(x)-acot(x))/x^3

Derivative of (sin(x)-acot(x))/x^3

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
sin(x) - acot(x)
----------------
        3       
       x
sin⁡(x)−acot⁡(x)x3\frac{\sin{\left(x \right)} - \operatorname{acot}{\left(x \right)}}{x^{3}} 
(sin(x) - acot(x))/x^3
The graph
02468-8-6-4-2-1010-100000100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1                                   
------ + cos(x)                       
     2                                
1 + x             3*(sin(x) - acot(x))
--------------- - --------------------
        3                   4         
       x                   x
cos⁡(x)+1x2+1x3−3(sin⁡(x)−acot⁡(x))x4\frac{\cos{\left(x \right)} + \frac{1}{x^{2} + 1}}{x^{3}} - \frac{3 \left(\sin{\left(x \right)} - \operatorname{acot}{\left(x \right)}\right)}{x^{4}}
Simplify
The second derivative [src] 
            /  1            \                                     
          6*|------ + cos(x)|                                     
            |     2         |                                     
            \1 + x          /      2*x      12*(-acot(x) + sin(x))
-sin(x) - ------------------- - --------- + ----------------------
                   x                    2              2          
                                /     2\              x           
                                \1 + x /                          
------------------------------------------------------------------
                                 3                                
                                x
−2x(x2+1)2−sin⁡(x)−6(cos⁡(x)+1x2+1)x+12(sin⁡(x)−acot⁡(x))x2x3\frac{- \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} - \frac{6 \left(\cos{\left(x \right)} + \frac{1}{x^{2} + 1}\right)}{x} + \frac{12 \left(\sin{\left(x \right)} - \operatorname{acot}{\left(x \right)}\right)}{x^{2}}}{x^{3}}
Simplify
The third derivative [src] 
                                                             /   2*x            \                       
                                                           9*|--------- + sin(x)|      /  1            \
                                                             |        2         |   36*|------ + cos(x)|
                                                     2       |/     2\          |      |     2         |
              2       60*(-acot(x) + sin(x))      8*x        \\1 + x /          /      \1 + x          /
-cos(x) - --------- - ---------------------- + --------- + ---------------------- + --------------------
                  2              3                     3             x                        2         
          /     2\              x              /     2\                                      x          
          \1 + x /                             \1 + x /                                                 
--------------------------------------------------------------------------------------------------------
                                                    3                                                   
                                                   x
8x2(x2+1)3−cos⁡(x)−2(x2+1)2+9(2x(x2+1)2+sin⁡(x))x+36(cos⁡(x)+1x2+1)x2−60(sin⁡(x)−acot⁡(x))x3x3\frac{\frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} - \cos{\left(x \right)} - \frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{9 \left(\frac{2 x}{\left(x^{2} + 1\right)^{2}} + \sin{\left(x \right)}\right)}{x} + \frac{36 \left(\cos{\left(x \right)} + \frac{1}{x^{2} + 1}\right)}{x^{2}} - \frac{60 \left(\sin{\left(x \right)} - \operatorname{acot}{\left(x \right)}\right)}{x^{3}}}{x^{3}}
Simplify
The graph
Derivative of (sin(x)-acot(x))/x^3
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