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The derivative of the function/ arcsin(ctg(3^x))

Derivative of arcsin(ctg(3^x))

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

The graph:

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The solution

You have entered [src] 
    /   / x\\
asin\cot\3 //
asin⁡(cot⁡(3x))\operatorname{asin}{\left(\cot{\left(3^{x} \right)} \right)} 
asin(cot(3^x))
The graph
02468-8-6-4-2-1010-100000100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x /        2/ x\\       
3 *\-1 - cot \3 //*log(3)
-------------------------
       ______________    
      /        2/ x\     
    \/  1 - cot \3 /
3x(−cot⁡2(3x)−1)log⁡(3)1−cot⁡2(3x)\frac{3^{x} \left(- \cot^{2}{\left(3^{x} \right)} - 1\right) \log{\left(3 \right)}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}
Simplify
The second derivative [src] 
                          /                     x /       2/ x\\    / x\\
 x    2    /       2/ x\\ |        x    / x\   3 *\1 + cot \3 //*cot\3 /|
3 *log (3)*\1 + cot \3 //*|-1 + 2*3 *cot\3 / + -------------------------|
                          |                                  2/ x\      |
                          \                           1 - cot \3 /      /
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                               ______________                            
                              /        2/ x\                             
                            \/  1 - cot \3 /
3x(cot⁡2(3x)+1)(2⋅3xcot⁡(3x)+3x(cot⁡2(3x)+1)cot⁡(3x)1−cot⁡2(3x)−1)log⁡(3)21−cot⁡2(3x)\frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \left(2 \cdot 3^{x} \cot{\left(3^{x} \right)} + \frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - 1\right) \log{\left(3 \right)}^{2}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}
Simplify
The third derivative [src] 
                          /                                                                                 2                                                         2                                       \
                          |                                                               2*x /       2/ x\\       2*x    2/ x\ /       2/ x\\      2*x /       2/ x\\     2/ x\      x /       2/ x\\    / x\|
 x    3    /       2/ x\\ |        2*x    2/ x\      2*x /       2/ x\\      x    / x\   3   *\1 + cot \3 //    6*3   *cot \3 /*\1 + cot \3 //   3*3   *\1 + cot \3 // *cot \3 /   3*3 *\1 + cot \3 //*cot\3 /|
3 *log (3)*\1 + cot \3 //*|-1 - 4*3   *cot \3 / - 2*3   *\1 + cot \3 // + 6*3 *cot\3 / - -------------------- - ------------------------------ - ------------------------------- + ---------------------------|
                          |                                                                         2/ x\                       2/ x\                                  2                          2/ x\       |
                          |                                                                  1 - cot \3 /                1 - cot \3 /                    /       2/ x\\                    1 - cot \3 /       |
                          \                                                                                                                              \1 - cot \3 //                                       /
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                                                                                                  ______________                                                                                               
                                                                                                 /        2/ x\                                                                                                
                                                                                               \/  1 - cot \3 /
3x(cot⁡2(3x)+1)(−2⋅32x(cot⁡2(3x)+1)−4⋅32xcot⁡2(3x)−32x(cot⁡2(3x)+1)21−cot⁡2(3x)−6⋅32x(cot⁡2(3x)+1)cot⁡2(3x)1−cot⁡2(3x)−3⋅32x(cot⁡2(3x)+1)2cot⁡2(3x)(1−cot⁡2(3x))2+6⋅3xcot⁡(3x)+3⋅3x(cot⁡2(3x)+1)cot⁡(3x)1−cot⁡2(3x)−1)log⁡(3)31−cot⁡2(3x)\frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \left(- 2 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) - 4 \cdot 3^{2 x} \cot^{2}{\left(3^{x} \right)} - \frac{3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right)^{2}}{1 - \cot^{2}{\left(3^{x} \right)}} - \frac{6 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot^{2}{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - \frac{3 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right)^{2} \cot^{2}{\left(3^{x} \right)}}{\left(1 - \cot^{2}{\left(3^{x} \right)}\right)^{2}} + 6 \cdot 3^{x} \cot{\left(3^{x} \right)} + \frac{3 \cdot 3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - 1\right) \log{\left(3 \right)}^{3}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}
Simplify
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