Mister Exam

Other calculators

The derivative of the function/ xarcsinx+sqrt1-x^2

Derivative of xarcsinx+sqrt1-x^2

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

The graph:

from to

Piecewise:

The solution

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