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The derivative of the function/ log3x·arcsinx

Derivative of log3x·arcsinx

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

The graph:

from to

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The solution

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