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The derivative of the function/ arccos(sqrt(tan(x)))

Derivative of arccos(sqrt(tan(x)))

Function f() - derivative -N order at the point
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    /  ________\
acos\\/ tan(x) /
acos⁡(tan⁡(x))\operatorname{acos}{\left(\sqrt{\tan{\left(x \right)}} \right)} 
acos(sqrt(tan(x)))
The graph
02468-8-6-4-2-10105-10
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      /       2   \      
      |1   tan (x)|      
     -|- + -------|      
      \2      2   /      
-------------------------
  ____________   ________
\/ 1 - tan(x) *\/ tan(x)
−tan⁡2(x)2+121−tan⁡(x)tan⁡(x)- \frac{\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}}{\sqrt{1 - \tan{\left(x \right)}} \sqrt{\tan{\left(x \right)}}}
Simplify
The second derivative [src] 
              /                      2                    2          \
/       2   \ |    ________   1 + tan (x)          1 + tan (x)       |
\1 + tan (x)/*|- \/ tan(x)  + ----------- - -------------------------|
              |                    3/2                       ________|
              \               4*tan   (x)   4*(1 - tan(x))*\/ tan(x) /
----------------------------------------------------------------------
                              ____________                            
                            \/ 1 - tan(x)
(tan⁡2(x)+1)(tan⁡2(x)+14tan⁡32(x)−tan⁡(x)−tan⁡2(x)+14(1−tan⁡(x))tan⁡(x))1−tan⁡(x)\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{4 \tan^{\frac{3}{2}}{\left(x \right)}} - \sqrt{\tan{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{4 \left(1 - \tan{\left(x \right)}\right) \sqrt{\tan{\left(x \right)}}}\right)}{\sqrt{1 - \tan{\left(x \right)}}}
Simplify
The third derivative [src] 
              /                                              2                                                    2                          2     \
              |                       2         /       2   \        ________ /       2   \          /       2   \              /       2   \      |
/       2   \ |       3/2      1 + tan (x)    3*\1 + tan (x)/    3*\/ tan(x) *\1 + tan (x)/        3*\1 + tan (x)/              \1 + tan (x)/      |
\1 + tan (x)/*|- 2*tan   (x) + ------------ - ---------------- - -------------------------- - -------------------------- + ------------------------|
              |                    ________          5/2               2*(1 - tan(x))                       2   ________                     3/2   |
              \                2*\/ tan(x)      8*tan   (x)                                   8*(1 - tan(x)) *\/ tan(x)    4*(1 - tan(x))*tan   (x)/
----------------------------------------------------------------------------------------------------------------------------------------------------
                                                                     ____________                                                                   
                                                                   \/ 1 - tan(x)
(tan⁡2(x)+1)(−3(tan⁡2(x)+1)28tan⁡52(x)+tan⁡2(x)+12tan⁡(x)−2tan⁡32(x)+(tan⁡2(x)+1)24(1−tan⁡(x))tan⁡32(x)−3(tan⁡2(x)+1)tan⁡(x)2(1−tan⁡(x))−3(tan⁡2(x)+1)28(1−tan⁡(x))2tan⁡(x))1−tan⁡(x)\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{8 \tan^{\frac{5}{2}}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1}{2 \sqrt{\tan{\left(x \right)}}} - 2 \tan^{\frac{3}{2}}{\left(x \right)} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{4 \left(1 - \tan{\left(x \right)}\right) \tan^{\frac{3}{2}}{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}}}{2 \left(1 - \tan{\left(x \right)}\right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{8 \left(1 - \tan{\left(x \right)}\right)^{2} \sqrt{\tan{\left(x \right)}}}\right)}{\sqrt{1 - \tan{\left(x \right)}}}
Simplify
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