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y=arctg^5(e^arcsinx^2)
Derivada de la función/ sinx^2/ arctg/ arcsin/ y=arctg^5(e^arcsinx^2)

Derivada de y=arctg^5(e^arcsinx^2)

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     /     2   \
    5| asin (x)|
atan \E        /
atan⁡5(easin⁡2(x))\operatorname{atan}^{5}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)} 
atan(E^(asin(x)^2))^5
Gráfica
02468-8-6-4-2-1010-5050
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Primera derivada [src] 
        /     2   \              2   
       4| asin (x)|          asin (x)
10*atan \E        /*asin(x)*e        
-------------------------------------
       ________ /           2   \    
      /      2  |     2*asin (x)|    
    \/  1 - x  *\1 + e          /
10easin⁡2(x)asin⁡(x)atan⁡4(easin⁡2(x))1−x2(e2asin⁡2(x)+1)\frac{10 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{4}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)}
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Segunda derivada [src] 
                    /      /     2   \                  /     2   \                 /     2   \                       2                        /     2   \        2   \          
        /     2   \ |      | asin (x)|         2        | asin (x)|                 | asin (x)|             2     asin (x)            2        | asin (x)|  2*asin (x)|      2   
       3| asin (x)| |  atan\E        /   2*asin (x)*atan\E        /   x*asin(x)*atan\E        /       8*asin (x)*e              4*asin (x)*atan\E        /*e          |  asin (x)
10*atan \E        /*|- --------------- - -------------------------- + ------------------------- - --------------------------- + --------------------------------------|*e        
                    |            2                      2                            3/2          /           2   \                  /           2   \                |          
                    |      -1 + x                 -1 + x                     /     2\             |     2*asin (x)| /      2\        |     2*asin (x)| /      2\      |          
                    \                                                        \1 - x /             \1 + e          /*\-1 + x /        \1 + e          /*\-1 + x /      /          
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                                                                                            2                                                                                    
                                                                                      2*asin (x)                                                                                 
                                                                                 1 + e
10(xasin⁡(x)atan⁡(easin⁡2(x))(1−x2)32−2asin⁡2(x)atan⁡(easin⁡2(x))x2−1−atan⁡(easin⁡2(x))x2−1+4e2asin⁡2(x)asin⁡2(x)atan⁡(easin⁡2(x))(x2−1)(e2asin⁡2(x)+1)−8easin⁡2(x)asin⁡2(x)(x2−1)(e2asin⁡2(x)+1))easin⁡2(x)atan⁡3(easin⁡2(x))e2asin⁡2(x)+1\frac{10 \left(\frac{x \operatorname{asin}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{x^{2} - 1} - \frac{\operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{x^{2} - 1} + \frac{4 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right) \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} - \frac{8 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)}}{\left(x^{2} - 1\right) \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)}\right) e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{atan}^{3}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1}
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Tercera derivada [src] 
                    /         /     2   \                   /     2   \          /     2   \                     /     2   \                             /     2   \                         2                          /     2   \        2                       /     2   \        2              /     2   \                2                     /     2   \      2                       /     2   \        2                      /     2   \      2                         /     2   \        2                        /     2   \      2   \          
        /     2   \ |        2| asin (x)|         3        2| asin (x)|         2| asin (x)|              2     2| asin (x)|                   2        2| asin (x)|             3     2*asin (x)              3        | asin (x)|  3*asin (x)          3        2| asin (x)|  2*asin (x)          2| asin (x)|          2*asin (x)                  | asin (x)|  asin (x)          3        2| asin (x)|  4*asin (x)          3        | asin (x)|  asin (x)            2        2| asin (x)|  2*asin (x)            2        | asin (x)|  asin (x)|      2   
       2| asin (x)| |3*x*atan \E        /   4*asin (x)*atan \E        /   7*atan \E        /*asin(x)   3*x *atan \E        /*asin(x)   6*x*asin (x)*atan \E        /      48*asin (x)*e                 96*asin (x)*atan\E        /*e             32*asin (x)*atan \E        /*e             12*atan \E        /*asin(x)*e             24*asin(x)*atan\E        /*e           32*asin (x)*atan \E        /*e             48*asin (x)*atan\E        /*e           12*x*asin (x)*atan \E        /*e             24*x*asin (x)*atan\E        /*e        |  asin (x)
10*atan \E        /*|-------------------- + --------------------------- + -------------------------- + ----------------------------- + ----------------------------- + ------------------------------ - --------------------------------------- - ---------------------------------------- - --------------------------------------- + ------------------------------------ + ---------------------------------------- + ------------------------------------- - ------------------------------------------ + ---------------------------------------|*e        
                    |              2                        3/2                          3/2                            5/2                               2                                         2                                     2                    3/2 /           2   \                      3/2 /           2   \                   3/2 /           2   \                                         2                    3/2 /           2   \              /           2   \          2                /           2   \          2     |          
                    |     /      2\                 /     2\                     /     2\                       /     2\                         /      2\                     3/2 /           2   \                 3/2 /           2   \             /     2\    |     2*asin (x)|              /     2\    |     2*asin (x)|           /     2\    |     2*asin (x)|                    3/2 /           2   \             /     2\    |     2*asin (x)|              |     2*asin (x)| /      2\                 |     2*asin (x)| /      2\      |          
                    |     \-1 + x /                 \1 - x /                     \1 - x /                       \1 - x /                         \-1 + x /             /     2\    |     2*asin (x)|         /     2\    |     2*asin (x)|             \1 - x /   *\1 + e          /              \1 - x /   *\1 + e          /           \1 - x /   *\1 + e          /            /     2\    |     2*asin (x)|             \1 - x /   *\1 + e          /              \1 + e          /*\-1 + x /                 \1 + e          /*\-1 + x /      |          
                    \                                                                                                                                                  \1 - x /   *\1 + e          /         \1 - x /   *\1 + e          /                                                                                                                                         \1 - x /   *\1 + e          /                                                                                                                                     /          
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                                                                                                                                                                                                                                                                                   2                                                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                             2*asin (x)                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                                                                        1 + e
10(3x2asin⁡(x)atan⁡2(easin⁡2(x))(1−x2)52+6xasin⁡2(x)atan⁡2(easin⁡2(x))(x2−1)2+3xatan⁡2(easin⁡2(x))(x2−1)2−12xe2asin⁡2(x)asin⁡2(x)atan⁡2(easin⁡2(x))(x2−1)2(e2asin⁡2(x)+1)+24xeasin⁡2(x)asin⁡2(x)atan⁡(easin⁡2(x))(x2−1)2(e2asin⁡2(x)+1)+4asin⁡3(x)atan⁡2(easin⁡2(x))(1−x2)32+7asin⁡(x)atan⁡2(easin⁡2(x))(1−x2)32−32e2asin⁡2(x)asin⁡3(x)atan⁡2(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)−12e2asin⁡2(x)asin⁡(x)atan⁡2(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)+48easin⁡2(x)asin⁡3(x)atan⁡(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)+24easin⁡2(x)asin⁡(x)atan⁡(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)+32e4asin⁡2(x)asin⁡3(x)atan⁡2(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)2−96e3asin⁡2(x)asin⁡3(x)atan⁡(easin⁡2(x))(1−x2)32(e2asin⁡2(x)+1)2+48e2asin⁡2(x)asin⁡3(x)(1−x2)32(e2asin⁡2(x)+1)2)easin⁡2(x)atan⁡2(easin⁡2(x))e2asin⁡2(x)+1\frac{10 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{12 x e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{24 x e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{4 \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{7 \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{32 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} - \frac{12 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{48 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{24 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{32 e^{4 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}} - \frac{96 e^{3 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}} + \frac{48 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}}\right) e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1}
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Gráfico
Derivada de y=arctg^5(e^arcsinx^2)
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