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y=ctg(√x)³×arcsin²x
Derivada de la función/ arcsin/ y=ctg/ sin²x/ y=ctg(√x)³×arcsin²x

Derivada de y=ctg(√x)³×arcsin²x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   3/  ___\     2   
cot \\/ x /*asin (x)
cot⁡3(x)asin⁡2(x)\cot^{3}{\left(\sqrt{x} \right)} \operatorname{asin}^{2}{\left(x \right)} 
cot(sqrt(x))^3*asin(x)^2
Gráfica
02468-8-6-4-2-101002
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Primera derivada [src] 
     3/  ___\                 2       2/  ___\ /        2/  ___\\
2*cot \\/ x /*asin(x)   3*asin (x)*cot \\/ x /*\-1 - cot \\/ x //
--------------------- + -----------------------------------------
        ________                             ___                 
       /      2                          2*\/ x                  
     \/  1 - x
2cot⁡3(x)asin⁡(x)1−x2+3(−cot⁡2(x)−1)cot⁡2(x)asin⁡2(x)2x\frac{2 \cot^{3}{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{3 \left(- \cot^{2}{\left(\sqrt{x} \right)} - 1\right) \cot^{2}{\left(\sqrt{x} \right)} \operatorname{asin}^{2}{\left(x \right)}}{2 \sqrt{x}}
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Segunda derivada [src] 
/                                                                       /   /  ___\        2/  ___\     /       2/  ___\\\                                         \           
|                                                2    /       2/  ___\\ |cot\\/ x /   2*cot \\/ x /   2*\1 + cot \\/ x //|                                         |           
|                                          3*asin (x)*\1 + cot \\/ x //*|---------- + ------------- + -------------------|                                         |           
|                                                                       |    3/2            x                  x         |     /       2/  ___\\            /  ___\|           
|     2/  ___\ /     1       x*asin(x) \                                \   x                                            /   6*\1 + cot \\/ x //*asin(x)*cot\\/ x /|    /  ___\
|2*cot \\/ x /*|- ------- + -----------| + ------------------------------------------------------------------------------- - --------------------------------------|*cot\\/ x /
|              |        2           3/2|                                          4                                                             ________           |           
|              |  -1 + x    /     2\   |                                                                                                 ___   /      2            |           
\              \            \1 - x /   /                                                                                               \/ x *\/  1 - x             /
(2(xasin⁡(x)(1−x2)32−1x2−1)cot⁡2(x)+3(cot⁡2(x)+1)(2(cot⁡2(x)+1)x+2cot⁡2(x)x+cot⁡(x)x32)asin⁡2(x)4−6(cot⁡2(x)+1)cot⁡(x)asin⁡(x)x1−x2)cot⁡(x)\left(2 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \cot^{2}{\left(\sqrt{x} \right)} + \frac{3 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)}{x} + \frac{2 \cot^{2}{\left(\sqrt{x} \right)}}{x} + \frac{\cot{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{4} - \frac{6 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{x} \sqrt{1 - x^{2}}}\right) \cot{\left(\sqrt{x} \right)}
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Tercera derivada [src] 
                                                                                       /                   2                                                                                                                    \                                                                                                                                                        
                                                                                       |  /       2/  ___\\         2/  ___\        4/  ___\        3/  ___\     /       2/  ___\\    /  ___\         2/  ___\ /       2/  ___\\|        2/  ___\ /       2/  ___\\ /     1       x*asin(x) \                       /   /  ___\        2/  ___\     /       2/  ___\\\                   
                                                                2    /       2/  ___\\ |2*\1 + cot \\/ x //    3*cot \\/ x /   4*cot \\/ x /   6*cot \\/ x /   6*\1 + cot \\/ x //*cot\\/ x /   14*cot \\/ x /*\1 + cot \\/ x //|   9*cot \\/ x /*\1 + cot \\/ x //*|- ------- + -----------|     /       2/  ___\\ |cot\\/ x /   2*cot \\/ x /   2*\1 + cot \\/ x //|            /  ___\
                                                          3*asin (x)*\1 + cot \\/ x //*|-------------------- + ------------- + ------------- + ------------- + ------------------------------ + --------------------------------|                                   |        2           3/2|   9*\1 + cot \\/ x //*|---------- + ------------- + -------------------|*asin(x)*cot\\/ x /
              /                              2        \                                |         3/2                 5/2             3/2              2                       2                                3/2              |                                   |  -1 + x    /     2\   |                       |    3/2            x                  x         |                   
     3/  ___\ |  asin(x)        3*x       3*x *asin(x)|                                \        x                   x               x                x                       x                                x                 /                                   \            \1 - x /   /                       \   x                                            /                   
2*cot \\/ x /*|----------- + ---------- + ------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------- + -----------------------------------------------------------------------------------------
              |        3/2            2           5/2 |                                                                                      8                                                                                                                  ___                                                                        ________                                      
              |/     2\      /      2\    /     2\    |                                                                                                                                                                                                       \/ x                                                                        /      2                                       
              \\1 - x /      \-1 + x /    \1 - x /    /                                                                                                                                                                                                                                                                               2*\/  1 - x
−3(cot⁡2(x)+1)(6(cot⁡2(x)+1)cot⁡(x)x2+6cot⁡3(x)x2+2(cot⁡2(x)+1)2x32+14(cot⁡2(x)+1)cot⁡2(x)x32+4cot⁡4(x)x32+3cot⁡2(x)x52)asin⁡2(x)8+2(3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32)cot⁡3(x)+9(cot⁡2(x)+1)(2(cot⁡2(x)+1)x+2cot⁡2(x)x+cot⁡(x)x32)cot⁡(x)asin⁡(x)21−x2−9(xasin⁡(x)(1−x2)32−1x2−1)(cot⁡2(x)+1)cot⁡2(x)x- \frac{3 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{6 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot{\left(\sqrt{x} \right)}}{x^{2}} + \frac{6 \cot^{3}{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)^{2}}{x^{\frac{3}{2}}} + \frac{14 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{4 \cot^{4}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3 \cot^{2}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{8} + 2 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \cot^{3}{\left(\sqrt{x} \right)} + \frac{9 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)}{x} + \frac{2 \cot^{2}{\left(\sqrt{x} \right)}}{x} + \frac{\cot{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \cot{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{2 \sqrt{1 - x^{2}}} - \frac{9 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot^{2}{\left(\sqrt{x} \right)}}{\sqrt{x}}
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Gráfico
Derivada de y=ctg(√x)³×arcsin²x
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