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y=arsin^lnx+1
Derivada de la función/ lnx+1/ y=arsin^lnx+1

Derivada de y=arsin^lnx+1

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    log(x)       
asin      (x) + 1
asin⁡log⁡(x)(x)+1\operatorname{asin}^{\log{\left(x \right)}}{\left(x \right)} + 1 
asin(x)^log(x) + 1
Solución detallada

  1. diferenciamos asin⁡log⁡(x)(x)+1\operatorname{asin}^{\log{\left(x \right)}}{\left(x \right)} + 1 miembro por miembro:

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

      Perola derivada

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

    2. La derivada de una constante 11 es igual a cero.

    Como resultado de: (log⁡(log⁡(x))+1)log⁡(x)log⁡(x)\left(\log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\log{\left(x \right)}}

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    log(x)    /log(asin(x))          log(x)      \
asin      (x)*|------------ + -------------------|
              |     x            ________        |
              |                 /      2         |
              \               \/  1 - x  *asin(x)/
(log⁡(x)1−x2asin⁡(x)+log⁡(asin⁡(x))x)asin⁡log⁡(x)(x)\left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right) \operatorname{asin}^{\log{\left(x \right)}}{\left(x \right)}
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Segunda derivada [src] 
              /                                    2                                                                                  \
    log(x)    |/log(asin(x))          log(x)      \    log(asin(x))         log(x)                   2                   x*log(x)     |
asin      (x)*||------------ + -------------------|  - ------------ + ------------------ + --------------------- + -------------------|
              ||     x            ________        |          2        /      2\     2           ________                   3/2        |
              ||                 /      2         |         x         \-1 + x /*asin (x)       /      2            /     2\           |
              \\               \/  1 - x  *asin(x)/                                        x*\/  1 - x  *asin(x)   \1 - x /   *asin(x)/
(xlog⁡(x)(1−x2)32asin⁡(x)+(log⁡(x)1−x2asin⁡(x)+log⁡(asin⁡(x))x)2+log⁡(x)(x2−1)asin⁡2(x)+2x1−x2asin⁡(x)−log⁡(asin⁡(x))x2)asin⁡log⁡(x)(x)\left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right)^{2} + \frac{\log{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{2}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{asin}^{\log{\left(x \right)}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
              /                                    3                                                                                                                                                                                                                                                                                                 2           \
    log(x)    |/log(asin(x))          log(x)      \    2*log(asin(x))            3              /log(asin(x))          log(x)      \ /  log(asin(x))         log(x)                   2                   x*log(x)     \          log(x)                   3                    2*log(x)                  3                  3*x*log(x)           3*x *log(x)    |
asin      (x)*||------------ + -------------------|  + -------------- + ------------------- + 3*|------------ + -------------------|*|- ------------ + ------------------ + --------------------- + -------------------| + ------------------- - ---------------------- + -------------------- + -------------------- - ------------------- + -------------------|
              ||     x            ________        |           3                 3/2             |     x            ________        | |        2        /      2\     2           ________                   3/2        |           3/2                 ________                   3/2              /      2\     2               2                    5/2        |
              ||                 /      2         |          x          /     2\                |                 /      2         | |       x         \-1 + x /*asin (x)       /      2            /     2\           |   /     2\               2   /      2            /     2\        3      x*\-1 + x /*asin (x)   /      2\      2      /     2\           |
              \\               \/  1 - x  *asin(x)/                     \1 - x /   *asin(x)     \               \/  1 - x  *asin(x)/ \                                      x*\/  1 - x  *asin(x)   \1 - x /   *asin(x)/   \1 - x /   *asin(x)   x *\/  1 - x  *asin(x)   \1 - x /   *asin (x)                          \-1 + x / *asin (x)   \1 - x /   *asin(x)/
(3x2log⁡(x)(1−x2)52asin⁡(x)−3xlog⁡(x)(x2−1)2asin⁡2(x)+(log⁡(x)1−x2asin⁡(x)+log⁡(asin⁡(x))x)3+3(log⁡(x)1−x2asin⁡(x)+log⁡(asin⁡(x))x)(xlog⁡(x)(1−x2)32asin⁡(x)+log⁡(x)(x2−1)asin⁡2(x)+2x1−x2asin⁡(x)−log⁡(asin⁡(x))x2)+log⁡(x)(1−x2)32asin⁡(x)+2log⁡(x)(1−x2)32asin⁡3(x)+3(1−x2)32asin⁡(x)+3x(x2−1)asin⁡2(x)−3x21−x2asin⁡(x)+2log⁡(asin⁡(x))x3)asin⁡log⁡(x)(x)\left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} - \frac{3 x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right)^{3} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{2}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{2}}\right) + \frac{\log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{3}{x \left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} - \frac{3}{x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{asin}^{\log{\left(x \right)}}{\left(x \right)}
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Gráfico
Derivada de y=arsin^lnx+1
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