Mister Exam

Derivative of asin(log(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
asin(log(x))
$$\operatorname{asin}{\left(\log{\left(x \right)} \right)}$$
asin(log(x))
The graph
The first derivative [src]
        1         
------------------
     _____________
    /        2    
x*\/  1 - log (x) 
$$\frac{1}{x \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The second derivative [src]
          log(x)   
  -1 + ----------- 
              2    
       1 - log (x) 
-------------------
      _____________
 2   /        2    
x *\/  1 - log (x) 
$$\frac{-1 + \frac{\log{\left(x \right)}}{1 - \log{\left(x \right)}^{2}}}{x^{2} \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The third derivative [src]
                                       2      
         1          3*log(x)      3*log (x)   
2 + ----------- - ----------- + --------------
           2             2                   2
    1 - log (x)   1 - log (x)   /       2   \ 
                                \1 - log (x)/ 
----------------------------------------------
                   _____________              
              3   /        2                  
             x *\/  1 - log (x)               
$$\frac{2 - \frac{3 \log{\left(x \right)}}{1 - \log{\left(x \right)}^{2}} + \frac{1}{1 - \log{\left(x \right)}^{2}} + \frac{3 \log{\left(x \right)}^{2}}{\left(1 - \log{\left(x \right)}^{2}\right)^{2}}}{x^{3} \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The graph
Derivative of asin(log(x))