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acos(x)*cot(x)
The derivative of the function/ acos(x)*cot(x)

Derivative of acos(x)*cot(x)

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

You have entered [src] 
acos(x)*cot(x)
cot⁡(x)acos⁡(x)\cot{\left(x \right)} \operatorname{acos}{\left(x \right)} 
acos(x)*cot(x)
The graph
02468-8-6-4-2-1010-200200
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
/        2   \              cot(x)  
\-1 - cot (x)/*acos(x) - -----------
                            ________
                           /      2 
                         \/  1 - x
(−cot⁡2(x)−1)acos⁡(x)−cot⁡(x)1−x2\left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{acos}{\left(x \right)} - \frac{\cot{\left(x \right)}}{\sqrt{1 - x^{2}}}
Simplify
The second derivative [src] 
  /       2   \                                               
2*\1 + cot (x)/     x*cot(x)      /       2   \               
--------------- - ----------- + 2*\1 + cot (x)/*acos(x)*cot(x)
     ________             3/2                                 
    /      2      /     2\                                    
  \/  1 - x       \1 - x /
−xcot⁡(x)(1−x2)32+2(cot⁡2(x)+1)cot⁡(x)acos⁡(x)+2(cot⁡2(x)+1)1−x2- \frac{x \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{acos}{\left(x \right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - x^{2}}}
Simplify
The third derivative [src] 
/          2 \                                                                                              
|       3*x  |                                                                                              
|-1 + -------|*cot(x)                                                                                       
|           2|            /       2   \                                                        /       2   \
\     -1 + x /          6*\1 + cot (x)/*cot(x)     /       2   \ /         2   \           3*x*\1 + cot (x)/
--------------------- - ---------------------- - 2*\1 + cot (x)/*\1 + 3*cot (x)/*acos(x) + -----------------
             3/2                ________                                                              3/2   
     /     2\                  /      2                                                       /     2\      
     \1 - x /                \/  1 - x                                                        \1 - x /
3x(cot⁡2(x)+1)(1−x2)32−2(cot⁡2(x)+1)(3cot⁡2(x)+1)acos⁡(x)−6(cot⁡2(x)+1)cot⁡(x)1−x2+(3x2x2−1−1)cot⁡(x)(1−x2)32\frac{3 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{acos}{\left(x \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of acos(x)*cot(x)
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