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Derivada de la función/ x^sin/ x^sinh(x^2/a)

Derivada de x^sinh(x^2/a)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     / 2\
     |x |
 sinh|--|
     \a /
x
xsinh⁡(x2a)x^{\sinh{\left(\frac{x^{2}}{a} \right)}} 
x^sinh(x^2/a)
Solución detallada

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

    Perola derivada

    (log⁡(sinh⁡(x2a))+1)sinh⁡sinh⁡(x2a)(x2a)\left(\log{\left(\sinh{\left(\frac{x^{2}}{a} \right)} \right)} + 1\right) \sinh^{\sinh{\left(\frac{x^{2}}{a} \right)}}{\left(\frac{x^{2}}{a} \right)}

  2. Simplificamos:

    (log⁡(sinh⁡(x2a))+1)sinh⁡sinh⁡(x2a)(x2a)\left(\log{\left(\sinh{\left(\frac{x^{2}}{a} \right)} \right)} + 1\right) \sinh^{\sinh{\left(\frac{x^{2}}{a} \right)}}{\left(\frac{x^{2}}{a} \right)}

Respuesta:

(log⁡(sinh⁡(x2a))+1)sinh⁡sinh⁡(x2a)(x2a)\left(\log{\left(\sinh{\left(\frac{x^{2}}{a} \right)} \right)} + 1\right) \sinh^{\sinh{\left(\frac{x^{2}}{a} \right)}}{\left(\frac{x^{2}}{a} \right)}

Primera derivada [src] 
     / 2\ /    / 2\           / 2\       \
     |x | |    |x |           |x |       |
 sinh|--| |sinh|--|   2*x*cosh|--|*log(x)|
     \a / |    \a /           \a /       |
x        *|-------- + -------------------|
          \   x                a         /
xsinh⁡(x2a)(sinh⁡(x2a)x+2xlog⁡(x)cosh⁡(x2a)a)x^{\sinh{\left(\frac{x^{2}}{a} \right)}} \left(\frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x} + \frac{2 x \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a}\right)
Simplificar
Segunda derivada [src] 
          /                                2                                                                   \
     / 2\ |/    / 2\           / 2\       \        / 2\         / 2\         / 2\                          / 2\|
     |x | ||    |x |           |x |       |        |x |         |x |         |x |             2            |x ||
 sinh|--| ||sinh|--|   2*x*cosh|--|*log(x)|    sinh|--|   4*cosh|--|   2*cosh|--|*log(x)   4*x *log(x)*sinh|--||
     \a / ||    \a /           \a /       |        \a /         \a /         \a /                          \a /|
x        *||-------- + -------------------|  - -------- + ---------- + ----------------- + --------------------|
          |\   x                a         /        2          a                a                     2         |
          \                                       x                                                 a          /
xsinh⁡(x2a)((sinh⁡(x2a)x+2xlog⁡(x)cosh⁡(x2a)a)2−sinh⁡(x2a)x2+2log⁡(x)cosh⁡(x2a)a+4cosh⁡(x2a)a+4x2log⁡(x)sinh⁡(x2a)a2)x^{\sinh{\left(\frac{x^{2}}{a} \right)}} \left(\left(\frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x} + \frac{2 x \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a}\right)^{2} - \frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x^{2}} + \frac{2 \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a} + \frac{4 \cosh{\left(\frac{x^{2}}{a} \right)}}{a} + \frac{4 x^{2} \log{\left(x \right)} \sinh{\left(\frac{x^{2}}{a} \right)}}{a^{2}}\right)
Simplificar
Tercera derivada [src] 
          /                                3                                                                                                                                                                                     \
     / 2\ |/    / 2\           / 2\       \          / 2\     /    / 2\           / 2\       \ /      / 2\         / 2\         / 2\                          / 2\\            / 2\            / 2\                          / 2\|
     |x | ||    |x |           |x |       |          |x |     |    |x |           |x |       | |      |x |         |x |         |x |             2            |x ||            |x |      3     |x |                          |x ||
 sinh|--| ||sinh|--|   2*x*cosh|--|*log(x)|    2*sinh|--|     |sinh|--|   2*x*cosh|--|*log(x)| |  sinh|--|   4*cosh|--|   2*cosh|--|*log(x)   4*x *log(x)*sinh|--||   12*x*sinh|--|   8*x *cosh|--|*log(x)   12*x*log(x)*sinh|--||
     \a / ||    \a /           \a /       |          \a /     |    \a /           \a /       | |      \a /         \a /         \a /                          \a /|            \a /            \a /                          \a /|
x        *||-------- + -------------------|  + ---------- + 3*|-------- + -------------------|*|- -------- + ---------- + ----------------- + --------------------| + ------------- + -------------------- + --------------------|
          |\   x                a         /         3         \   x                a         / |      2          a                a                     2         |          2                  3                      2         |
          \                                        x                                           \     x                                                 a          /         a                  a                      a          /
xsinh⁡(x2a)((sinh⁡(x2a)x+2xlog⁡(x)cosh⁡(x2a)a)3+3(sinh⁡(x2a)x+2xlog⁡(x)cosh⁡(x2a)a)(−sinh⁡(x2a)x2+2log⁡(x)cosh⁡(x2a)a+4cosh⁡(x2a)a+4x2log⁡(x)sinh⁡(x2a)a2)+2sinh⁡(x2a)x3+12xlog⁡(x)sinh⁡(x2a)a2+12xsinh⁡(x2a)a2+8x3log⁡(x)cosh⁡(x2a)a3)x^{\sinh{\left(\frac{x^{2}}{a} \right)}} \left(\left(\frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x} + \frac{2 x \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a}\right)^{3} + 3 \left(\frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x} + \frac{2 x \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a}\right) \left(- \frac{\sinh{\left(\frac{x^{2}}{a} \right)}}{x^{2}} + \frac{2 \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a} + \frac{4 \cosh{\left(\frac{x^{2}}{a} \right)}}{a} + \frac{4 x^{2} \log{\left(x \right)} \sinh{\left(\frac{x^{2}}{a} \right)}}{a^{2}}\right) + \frac{2 \sinh{\left(\frac{x^{2}}{a} \right)}}{x^{3}} + \frac{12 x \log{\left(x \right)} \sinh{\left(\frac{x^{2}}{a} \right)}}{a^{2}} + \frac{12 x \sinh{\left(\frac{x^{2}}{a} \right)}}{a^{2}} + \frac{8 x^{3} \log{\left(x \right)} \cosh{\left(\frac{x^{2}}{a} \right)}}{a^{3}}\right)
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