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y=3^arcsin√x^3+1
Derivada de la función/ sin√x/ x^3+1/ arcsin/ y=3^arcsin√x^3+1

Derivada de y=3^arcsin√x^3+1

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

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Solución

Ha introducido [src] 
     3/  ___\    
 asin \\/ x /    
3             + 1
3asin⁡3(x)+13^{\operatorname{asin}^{3}{\left(\sqrt{x} \right)}} + 1 
3^(asin(sqrt(x))^3) + 1
Gráfica
02468-8-6-4-2-10100100
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Primera derivada [src] 
       3/  ___\                    
   asin \\/ x /     2/  ___\       
3*3            *asin \\/ x /*log(3)
-----------------------------------
             ___   _______         
         2*\/ x *\/ 1 - x
3⋅3asin⁡3(x)log⁡(3)asin⁡2(x)2x1−x\frac{3 \cdot 3^{\operatorname{asin}^{3}{\left(\sqrt{x} \right)}} \log{\left(3 \right)} \operatorname{asin}^{2}{\left(\sqrt{x} \right)}}{2 \sqrt{x} \sqrt{1 - x}}
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Segunda derivada [src] 
       3/  ___\ /                     /  ___\           /  ___\           3/  ___\       \                   
   asin \\/ x / |      2          asin\\/ x /       asin\\/ x /     3*asin \\/ x /*log(3)|     /  ___\       
3*3            *|- ---------- + ---------------- - -------------- - ---------------------|*asin\\/ x /*log(3)
                |  x*(-1 + x)     ___        3/2    3/2   _______         x*(-1 + x)     |                   
                \               \/ x *(1 - x)      x   *\/ 1 - x                         /                   
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                                                      4
3⋅3asin⁡3(x)(−3log⁡(3)asin⁡3(x)x(x−1)−2x(x−1)+asin⁡(x)x(1−x)32−asin⁡(x)x321−x)log⁡(3)asin⁡(x)4\frac{3 \cdot 3^{\operatorname{asin}^{3}{\left(\sqrt{x} \right)}} \left(- \frac{3 \log{\left(3 \right)} \operatorname{asin}^{3}{\left(\sqrt{x} \right)}}{x \left(x - 1\right)} - \frac{2}{x \left(x - 1\right)} + \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(1 - x\right)^{\frac{3}{2}}} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sqrt{1 - x}}\right) \log{\left(3 \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4}
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Tercera derivada [src] 
       3/  ___\ /                         2/  ___\         2/  ___\          2/  ___\          /  ___\         /  ___\         4/  ___\                4/  ___\                6/  ___\    2             3/  ___\       \       
   asin \\/ x / |       2           2*asin \\/ x /   3*asin \\/ x /    3*asin \\/ x /    6*asin\\/ x /   6*asin\\/ x /   9*asin \\/ x /*log(3)   9*asin \\/ x /*log(3)   9*asin \\/ x /*log (3)   18*asin \\/ x /*log(3)|       
3*3            *|--------------- - --------------- + -------------- + ---------------- + ------------- + ------------- + --------------------- + --------------------- + ---------------------- + ----------------------|*log(3)
                | 3/2        3/2    3/2        3/2    5/2   _______     ___        5/2              2      2                            2              2                     3/2        3/2           3/2        3/2    |       
                \x   *(1 - x)      x   *(1 - x)      x   *\/ 1 - x    \/ x *(1 - x)       x*(-1 + x)      x *(-1 + x)         x*(-1 + x)              x *(-1 + x)           x   *(1 - x)             x   *(1 - x)       /       
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                                                                                                               8
3⋅3asin⁡3(x)(9log⁡(3)asin⁡4(x)x(x−1)2+6asin⁡(x)x(x−1)2+9log⁡(3)asin⁡4(x)x2(x−1)+6asin⁡(x)x2(x−1)+3asin⁡2(x)x(1−x)52+9log⁡(3)2asin⁡6(x)x32(1−x)32+18log⁡(3)asin⁡3(x)x32(1−x)32−2asin⁡2(x)x32(1−x)32+2x32(1−x)32+3asin⁡2(x)x521−x)log⁡(3)8\frac{3 \cdot 3^{\operatorname{asin}^{3}{\left(\sqrt{x} \right)}} \left(\frac{9 \log{\left(3 \right)} \operatorname{asin}^{4}{\left(\sqrt{x} \right)}}{x \left(x - 1\right)^{2}} + \frac{6 \operatorname{asin}{\left(\sqrt{x} \right)}}{x \left(x - 1\right)^{2}} + \frac{9 \log{\left(3 \right)} \operatorname{asin}^{4}{\left(\sqrt{x} \right)}}{x^{2} \left(x - 1\right)} + \frac{6 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2} \left(x - 1\right)} + \frac{3 \operatorname{asin}^{2}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(1 - x\right)^{\frac{5}{2}}} + \frac{9 \log{\left(3 \right)}^{2} \operatorname{asin}^{6}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{18 \log{\left(3 \right)} \operatorname{asin}^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} - \frac{2 \operatorname{asin}^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{2}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{3 \operatorname{asin}^{2}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} \sqrt{1 - x}}\right) \log{\left(3 \right)}}{8}
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Gráfico
Derivada de y=3^arcsin√x^3+1
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