Mister Exam

Other calculators

The derivative of the function/ arcsin(sqrtx)*lnx

Derivative of arcsin(sqrtx)*lnx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    /  ___\       
asin\\/ x /*log(x)
log⁡(x)asin⁡(x)\log{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} 
asin(sqrt(x))*log(x)
The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    /  ___\                    
asin\\/ x /         log(x)     
----------- + -----------------
     x            ___   _______
              2*\/ x *\/ 1 - x
asin⁡(x)x+log⁡(x)2x1−x\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{2 \sqrt{x} \sqrt{1 - x}}
Simplify
The second derivative [src] 
                               /1     1   \       
                     /  ___\   |- + ------|*log(x)
      1          asin\\/ x /   \x   -1 + x/       
-------------- - ----------- - -------------------
 3/2   _______         2            ___   _______ 
x   *\/ 1 - x         x         4*\/ x *\/ 1 - x
−asin⁡(x)x2−(1x−1+1x)log⁡(x)4x1−x+1x321−x- \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \log{\left(x \right)}}{4 \sqrt{x} \sqrt{1 - x}} + \frac{1}{x^{\frac{3}{2}} \sqrt{1 - x}}
Simplify
The third derivative [src] 
                                                      /3        3           2     \       
                                      /1     1   \    |-- + --------- + ----------|*log(x)
      /  ___\                       3*|- + ------|    | 2           2   x*(-1 + x)|       
2*asin\\/ x /          3              \x   -1 + x/    \x    (-1 + x)              /       
------------- - ---------------- - ---------------- + ------------------------------------
       3           5/2   _______      3/2   _______                ___   _______          
      x         2*x   *\/ 1 - x    4*x   *\/ 1 - x             8*\/ x *\/ 1 - x
2asin⁡(x)x3+(3(x−1)2+2x(x−1)+3x2)log⁡(x)8x1−x−3(1x−1+1x)4x321−x−32x521−x\frac{2 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{3}} + \frac{\left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) \log{\left(x \right)}}{8 \sqrt{x} \sqrt{1 - x}} - \frac{3 \left(\frac{1}{x - 1} + \frac{1}{x}\right)}{4 x^{\frac{3}{2}} \sqrt{1 - x}} - \frac{3}{2 x^{\frac{5}{2}} \sqrt{1 - x}}
Simplify
    © Mister Exam – Calculator