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y=(e^x^2)arcsin3x
The derivative of the function/ y=(e^x^2)arcsin3x

Derivative of y=(e^x^2)arcsin3x

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

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The solution

You have entered [src] 
 / 2\          
 \x /          
e    *asin(3*x)
ex2asin⁡(3x)e^{x^{2}} \operatorname{asin}{\left(3 x \right)} 
  / / 2\          \
d | \x /          |
--\e    *asin(3*x)/
dx
ddxex2asin⁡(3x)\frac{d}{d x} e^{x^{2}} \operatorname{asin}{\left(3 x \right)}
Transform
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      / 2\                         
      \x /                     / 2\
   3*e                         \x /
------------- + 2*x*asin(3*x)*e    
   __________                      
  /        2                       
\/  1 - 9*x
2xex2asin⁡(3x)+3ex21−9x22 x e^{x^{2}} \operatorname{asin}{\left(3 x \right)} + \frac{3 e^{x^{2}}}{\sqrt{1 - 9 x^{2}}}
Simplify
The second derivative [src] 
                                                          / 2\
/  /       2\                  12*x            27*x    \  \x /
|2*\1 + 2*x /*asin(3*x) + ------------- + -------------|*e    
|                            __________             3/2|      
|                           /        2    /       2\   |      
\                         \/  1 - 9*x     \1 - 9*x /   /
(12x1−9x2+27x(1−9x2)32+2⋅(2x2+1)asin⁡(3x))ex2\left(\frac{12 x}{\sqrt{1 - 9 x^{2}}} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 2 \cdot \left(2 x^{2} + 1\right) \operatorname{asin}{\left(3 x \right)}\right) e^{x^{2}}
Simplify
The third derivative [src] 
/     /           2  \                                                           \      
|     |       27*x   |                                                           |      
|  27*|-1 + ---------|                                                           |      
|     |             2|      /       2\            2                              |  / 2\
|     \     -1 + 9*x /   18*\1 + 2*x /       162*x           /       2\          |  \x /
|- ------------------- + ------------- + ------------- + 4*x*\3 + 2*x /*asin(3*x)|*e    
|               3/2         __________             3/2                           |      
|     /       2\           /        2    /       2\                              |      
\     \1 - 9*x /         \/  1 - 9*x     \1 - 9*x /                              /
(162x2(1−9x2)32+4x(2x2+3)asin⁡(3x)+18⋅(2x2+1)1−9x2−27⋅(27x29x2−1−1)(1−9x2)32)ex2\left(\frac{162 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 4 x \left(2 x^{2} + 3\right) \operatorname{asin}{\left(3 x \right)} + \frac{18 \cdot \left(2 x^{2} + 1\right)}{\sqrt{1 - 9 x^{2}}} - \frac{27 \cdot \left(\frac{27 x^{2}}{9 x^{2} - 1} - 1\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) e^{x^{2}}
Simplify
The graph
Derivative of y=(e^x^2)arcsin3x
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