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The derivative of the function/ arcctg(sqrt(x))/lnx+1

Derivative of arcctg(sqrt(x))/lnx+1

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

The graph:

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The solution

You have entered [src] 
    /  ___\    
acot\\/ x /    
----------- + 1
   log(x)
$$1 + \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{\log{\left(x \right)}}$$ 
acot(sqrt(x))/log(x) + 1
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      /  ___\                         
  acot\\/ x /             1           
- ----------- - ----------------------
        2           ___               
   x*log (x)    2*\/ x *(1 + x)*log(x)
$$- \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{x \log{\left(x \right)}^{2}} - \frac{1}{2 \sqrt{x} \left(x + 1\right) \log{\left(x \right)}}$$
Simplify
The second derivative [src] 
                                        /  ___\                               /  ___\
       1                 1          acot\\/ x /            1            2*acot\\/ x /
---------------- + -------------- + ----------- + ------------------- + -------------
    ___        2      3/2             2            3/2                     2    2    
2*\/ x *(1 + x)    4*x   *(1 + x)    x *log(x)    x   *(1 + x)*log(x)     x *log (x) 
-------------------------------------------------------------------------------------
                                        log(x)
$$\frac{\frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{x^{2} \log{\left(x \right)}} + \frac{2 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{1}{2 \sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{4 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}} \left(x + 1\right) \log{\left(x \right)}}}{\log{\left(x \right)}}$$
Simplify
The third derivative [src] 
 /                                                          /  ___\                                /  ___\         /  ___\                                                 \ 
 |      1                 1                3          2*acot\\/ x /            3             6*acot\\/ x /   6*acot\\/ x /             3                        9          | 
-|-------------- + --------------- + -------------- + ------------- + -------------------- + ------------- + ------------- + ---------------------- + ---------------------| 
 |  ___        3      3/2        2      5/2              3             5/2            2         3    3          3    2          3/2        2             5/2               | 
 \\/ x *(1 + x)    2*x   *(1 + x)    8*x   *(1 + x)     x *log(x)     x   *(1 + x)*log (x)     x *log (x)      x *log (x)    2*x   *(1 + x) *log(x)   4*x   *(1 + x)*log(x)/ 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    log(x)
$$- \frac{\frac{2 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}} + \frac{6 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{6 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}^{3}} + \frac{1}{\sqrt{x} \left(x + 1\right)^{3}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2} \log{\left(x \right)}} + \frac{3}{8 x^{\frac{5}{2}} \left(x + 1\right)} + \frac{9}{4 x^{\frac{5}{2}} \left(x + 1\right) \log{\left(x \right)}} + \frac{3}{x^{\frac{5}{2}} \left(x + 1\right) \log{\left(x \right)}^{2}}}{\log{\left(x \right)}}$$
Simplify
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