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Derivada de √x
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Expresiones idénticas
(arcsin2x)^(ctg(x+ uno))
(arc seno de 2x) en el grado (ctg(x más 1))
(arc seno de 2x) en el grado (ctg(x más uno))
(arcsin2x)(ctg(x+1))
arcsin2xctgx+1
arcsin2x^ctgx+1
Expresiones semejantes
(arcsin2x)^(ctg(x-1))
Expresiones con funciones
ctg
ctg(x^2)
ctg(x/7)

Derivada de la función/ arcsin/ sin2x/ (x+1)/ (arcsin2x)^(ctg(x+1))

Derivada de (arcsin2x)^(ctg(x+1))

Solución

Ha introducido [src]

    cot(x + 1)     
asin          (2*x)

\operatorname{asin}^{\cot{\left(x + 1 \right)}}{\left(2 x \right)}

asin(2*x)^cot(x + 1)

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

$\left(\log{\left(\cot{\left(x + 1 \right)} \right)} + 1\right) \cot^{\cot{\left(x + 1 \right)}}{\left(x + 1 \right)}$
Simplificamos:

$\left(\log{\left(\cot{\left(x + 1 \right)} \right)} + 1\right) \cot^{\cot{\left(x + 1 \right)}}{\left(x + 1 \right)}$

Respuesta:

$\left(\log{\left(\cot{\left(x + 1 \right)} \right)} + 1\right) \cot^{\cot{\left(x + 1 \right)}}{\left(x + 1 \right)}$

Primera derivada [src]

    cot(x + 1)      //        2       \                        2*cot(x + 1)     \
asin          (2*x)*|\-1 - cot (x + 1)/*log(asin(2*x)) + -----------------------|
                    |                                       __________          |
                    |                                      /        2           |
                    \                                    \/  1 - 4*x  *asin(2*x)/

\left(\left(- \cot^{2}{\left(x + 1 \right)} - 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} + \frac{2 \cot{\left(x + 1 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) \operatorname{asin}^{\cot{\left(x + 1 \right)}}{\left(2 x \right)}

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Segunda derivada [src]

                    /                                                            2       /       2       \                                                                                                     \
    cot(1 + x)      |//       2       \                        2*cot(1 + x)     \      4*\1 + cot (1 + x)/       /       2       \                                  4*cot(1 + x)             8*x*cot(1 + x)    |
asin          (2*x)*||\1 + cot (1 + x)/*log(asin(2*x)) - -----------------------|  - ----------------------- + 2*\1 + cot (1 + x)/*cot(1 + x)*log(asin(2*x)) + ---------------------- + -----------------------|
                    ||                                      __________          |       __________                                                             /        2\     2                  3/2          |
                    ||                                     /        2           |      /        2                                                              \-1 + 4*x /*asin (2*x)   /       2\             |
                    \\                                   \/  1 - 4*x  *asin(2*x)/    \/  1 - 4*x  *asin(2*x)                                                                            \1 - 4*x /   *asin(2*x)/

\left(\frac{8 x \cot{\left(x + 1 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \left(\left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} - \frac{2 \cot{\left(x + 1 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right)^{2} + 2 \left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} \cot{\left(x + 1 \right)} + \frac{4 \cot{\left(x + 1 \right)}}{\left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} - \frac{4 \left(\cot^{2}{\left(x + 1 \right)} + 1\right)}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) \operatorname{asin}^{\cot{\left(x + 1 \right)}}{\left(2 x \right)}

Simplificar

Tercera derivada [src]

                     /                                                            3                      2                                                                                 /                                                  /       2       \                                                     \                                                                                                             /       2       \            2                    /       2       \                    /       2       \                          \
     cot(1 + x)      |//       2       \                        2*cot(1 + x)     \      /       2       \                     //       2       \                        2*cot(1 + x)     \ |/       2       \                               2*\1 + cot (1 + x)/          2*cot(1 + x)             4*x*cot(1 + x)    |        16*cot(1 + x)               8*cot(1 + x)             2        /       2       \                   12*\1 + cot (1 + x)/        96*x *cot(1 + x)      12*\1 + cot (1 + x)/*cot(1 + x)    24*x*\1 + cot (1 + x)/       48*x*cot(1 + x)    |
-asin          (2*x)*||\1 + cot (1 + x)/*log(asin(2*x)) - -----------------------|  + 2*\1 + cot (1 + x)/ *log(asin(2*x)) + 6*|\1 + cot (1 + x)/*log(asin(2*x)) - -----------------------|*|\1 + cot (1 + x)/*cot(1 + x)*log(asin(2*x)) - ----------------------- + ---------------------- + -----------------------| - ------------------------ - ----------------------- + 4*cot (1 + x)*\1 + cot (1 + x)/*log(asin(2*x)) + ---------------------- - ----------------------- - ------------------------------- + ----------------------- + -----------------------|
                     ||                                      __________          |                                            |                                      __________          | |                                                 __________             /        2\     2                  3/2          |             3/2                        3/2                                                              /        2\     2                  5/2                    __________                           3/2                        2           |
                     ||                                     /        2           |                                            |                                     /        2           | |                                                /        2              \-1 + 4*x /*asin (2*x)   /       2\             |   /       2\        3        /       2\                                                                 \-1 + 4*x /*asin (2*x)   /       2\                      /        2                  /       2\                /        2\      2     |
                     \\                                   \/  1 - 4*x  *asin(2*x)/                                            \                                   \/  1 - 4*x  *asin(2*x)/ \                                              \/  1 - 4*x  *asin(2*x)                            \1 - 4*x /   *asin(2*x)/   \1 - 4*x /   *asin (2*x)   \1 - 4*x /   *asin(2*x)                                                                             \1 - 4*x /   *asin(2*x)       \/  1 - 4*x  *asin(2*x)       \1 - 4*x /   *asin(2*x)   \-1 + 4*x / *asin (2*x)/

- \left(- \frac{96 x^{2} \cot{\left(x + 1 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(2 x \right)}} + \frac{48 x \cot{\left(x + 1 \right)}}{\left(4 x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(2 x \right)}} + \frac{24 x \left(\cot^{2}{\left(x + 1 \right)} + 1\right)}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \left(\left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} - \frac{2 \cot{\left(x + 1 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right)^{3} + 6 \left(\left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} - \frac{2 \cot{\left(x + 1 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) \left(\frac{4 x \cot{\left(x + 1 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} \cot{\left(x + 1 \right)} + \frac{2 \cot{\left(x + 1 \right)}}{\left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} - \frac{2 \left(\cot^{2}{\left(x + 1 \right)} + 1\right)}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) + 2 \left(\cot^{2}{\left(x + 1 \right)} + 1\right)^{2} \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} + 4 \left(\cot^{2}{\left(x + 1 \right)} + 1\right) \log{\left(\operatorname{asin}{\left(2 x \right)} \right)} \cot^{2}{\left(x + 1 \right)} + \frac{12 \left(\cot^{2}{\left(x + 1 \right)} + 1\right)}{\left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} - \frac{12 \left(\cot^{2}{\left(x + 1 \right)} + 1\right) \cot{\left(x + 1 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}} - \frac{8 \cot{\left(x + 1 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} - \frac{16 \cot{\left(x + 1 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(2 x \right)}}\right) \operatorname{asin}^{\cot{\left(x + 1 \right)}}{\left(2 x \right)}

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Derivada de (arcsin2x)^(ctg(x+1))

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