Mister Exam

Other calculators

The derivative of the function/ arsinx*(x*x+1)

Derivative of arsinx*(x*x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
asin(x)*(x*x + 1)
$$\left(x x + 1\right) \operatorname{asin}{\left(x \right)}$$ 
asin(x)*(x*x + 1)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  x*x + 1                
----------- + 2*x*asin(x)
   ________              
  /      2               
\/  1 - x
$$2 x \operatorname{asin}{\left(x \right)} + \frac{x x + 1}{\sqrt{1 - x^{2}}}$$
Simplify
The second derivative [src] 
                             /     2\
                4*x        x*\1 + x /
2*asin(x) + ----------- + -----------
               ________           3/2
              /      2    /     2\   
            \/  1 - x     \1 - x /
$$\frac{4 x}{\sqrt{1 - x^{2}}} + \frac{x \left(x^{2} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \operatorname{asin}{\left(x \right)}$$
Simplify
The third derivative [src] 
                      /          2 \
             /     2\ |       3*x  |
             \1 + x /*|-1 + -------|
        2             |           2|
     6*x              \     -1 + x /
6 + ------ - -----------------------
         2                 2        
    1 - x             1 - x         
------------------------------------
               ________             
              /      2              
            \/  1 - x
$$\frac{\frac{6 x^{2}}{1 - x^{2}} + 6 - \frac{\left(x^{2} + 1\right) \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{1 - x^{2}}}{\sqrt{1 - x^{2}}}$$
Simplify
    © Mister Exam – Calculator