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The derivative of the function/ e^x*arccosx

Derivative of e^x*arccosx

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

The graph:

from to

Piecewise:

The solution

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