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The derivative of the function/ arccosx/(x+1)

Derivative of arccosx/(x+1)

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

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The solution

You have entered [src] 
acos(x)
-------
 x + 1
acos⁡(x)x+1\frac{\operatorname{acos}{\left(x \right)}}{x + 1} 
acos(x)/(x + 1)
The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           1            acos(x) 
- ------------------- - --------
     ________                  2
    /      2            (x + 1) 
  \/  1 - x  *(x + 1)
−acos⁡(x)(x+1)2−11−x2(x+1)- \frac{\operatorname{acos}{\left(x \right)}}{\left(x + 1\right)^{2}} - \frac{1}{\sqrt{1 - x^{2}} \left(x + 1\right)}
Simplify
The second derivative [src] 
       x                 2            2*acos(x)
- ----------- + ------------------- + ---------
          3/2              ________           2
  /     2\                /      2     (1 + x) 
  \1 - x /      (1 + x)*\/  1 - x              
-----------------------------------------------
                     1 + x
−x(1−x2)32+2acos⁡(x)(x+1)2+21−x2(x+1)x+1\frac{- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \operatorname{acos}{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{2}{\sqrt{1 - x^{2}} \left(x + 1\right)}}{x + 1}
Simplify
The third derivative [src] 
          2                                                          
       3*x                                                           
-1 + -------                                                         
           2                                                         
     -1 + x    6*acos(x)            6                     3*x        
------------ - --------- - -------------------- + -------------------
        3/2            3               ________                   3/2
/     2\        (1 + x)           2   /      2            /     2\   
\1 - x /                   (1 + x) *\/  1 - x     (1 + x)*\1 - x /   
---------------------------------------------------------------------
                                1 + x
3x(1−x2)32(x+1)−6acos⁡(x)(x+1)3−61−x2(x+1)2+3x2x2−1−1(1−x2)32x+1\frac{\frac{3 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x + 1\right)} - \frac{6 \operatorname{acos}{\left(x \right)}}{\left(x + 1\right)^{3}} - \frac{6}{\sqrt{1 - x^{2}} \left(x + 1\right)^{2}} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{x + 1}
Simplify
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