Solución detallada
Tenemos la ecuación:
$$z = e^{\frac{- x^{3} - 2 x}{\sqrt{y + \tan{\left(y \right)}}}}$$
cambiamos:
$$z = e^{\frac{x \left(- x^{2} - 2\right)}{\sqrt{y + \tan{\left(y \right)}}}}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
z = expx*-2+x+2sqrty+tan+y))
Obtenemos la respuesta: z = exp(x*(-2 - x^2)/sqrt(y + tan(y)))
Suma y producto de raíces
[src]
/ x \ 2 / x \ 2 / x \ / x \ / x \ 2 / x \ 2 / x \ / x \
- 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x) - 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x)
| ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________|
/ / x \ 2 / x \ 2 / x \ / x \\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / / / x \ 2 / x \ 2 / x \ / x \\
cos|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||*e - I*e *sin|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||
| | ____________| | ____________| | ____________| | ____________|| | | ____________| | ____________| | ____________| | ____________||
\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) // \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) //
$$- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)}$$
/ x \ 2 / x \ 2 / x \ / x \ / x \ 2 / x \ 2 / x \ / x \
- 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x) - 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x)
| ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________|
/ / x \ 2 / x \ 2 / x \ / x \\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / / / x \ 2 / x \ 2 / x \ / x \\
cos|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||*e - I*e *sin|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||
| | ____________| | ____________| | ____________| | ____________|| | | ____________| | ____________| | ____________| | ____________||
\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) // \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) //
$$- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)}$$
/ x \ 2 / x \ 2 / x \ / x \ / x \ 2 / x \ 2 / x \ / x \
- 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x) - 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x)
| ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________|
/ / x \ 2 / x \ 2 / x \ / x \\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / / / x \ 2 / x \ 2 / x \ / x \\
cos|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||*e - I*e *sin|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||
| | ____________| | ____________| | ____________| | ____________|| | | ____________| | ____________| | ____________| | ____________||
\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) // \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) //
$$- i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)}$$
/ x \ 2 / x \ 2 / x \ / x \
- 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x)
| ____________| | ____________| | ____________| | ____________|
/ / / x \ 2 / x \ 2 / x \ / x \\ / / x \ 2 / x \ 2 / x \ / x \\\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) /
|- I*sin|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------|| + cos|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------|||*e
| | | ____________| | ____________| | ____________| | ____________|| | | ____________| | ____________| | ____________| | ____________|||
\ \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) // \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) ///
$$\left(- i \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)} + \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)}\right) e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}}$$
(-i*sin(2*im(x/sqrt(y + tan(y))) + re(x)^2*im(x/sqrt(y + tan(y))) - im(x)^2*im(x/sqrt(y + tan(y))) + 2*im(x)*re(x)*re(x/sqrt(y + tan(y)))) + cos(2*im(x/sqrt(y + tan(y))) + re(x)^2*im(x/sqrt(y + tan(y))) - im(x)^2*im(x/sqrt(y + tan(y))) + 2*im(x)*re(x)*re(x/sqrt(y + tan(y)))))*exp(-2*re(x/sqrt(y + tan(y))) + im(x)^2*re(x/sqrt(y + tan(y))) - re(x)^2*re(x/sqrt(y + tan(y))) + 2*im(x)*im(x/sqrt(y + tan(y)))*re(x))
/ x \ 2 / x \ 2 / x \ / x \ / x \ 2 / x \ 2 / x \ / x \
- 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x) - 2*re|--------------| + im (x)*re|--------------| - re (x)*re|--------------| + 2*im(x)*im|--------------|*re(x)
| ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________| | ____________|
/ / x \ 2 / x \ 2 / x \ / x \\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / / / x \ 2 / x \ 2 / x \ / x \\
z1 = cos|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||*e - I*e *sin|2*im|--------------| + re (x)*im|--------------| - im (x)*im|--------------| + 2*im(x)*re(x)*re|--------------||
| | ____________| | ____________| | ____________| | ____________|| | | ____________| | ____________| | ____________| | ____________||
\ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) // \ \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) / \\/ y + tan(y) //
$$z_{1} = - i e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)} + e^{- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{re}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} + 2 \operatorname{im}{\left(\frac{x}{\sqrt{y + \tan{\left(y \right)}}}\right)} \right)}$$
z1 = -i*exp(-re(x)^2*re(x/sqrt(y + tan(y))) + 2*re(x)*im(x)*im(x/sqrt(y + tan(y))) + re(x/sqrt(y + tan(y)))*im(x)^2 - 2*re(x/sqrt(y + tan(y))))*sin(re(x)^2*im(x/sqrt(y + tan(y))) + 2*re(x)*re(x/sqrt(y + tan(y)))*im(x) - im(x)^2*im(x/sqrt(y + tan(y))) + 2*im(x/sqrt(y + tan(y)))) + exp(-re(x)^2*re(x/sqrt(y + tan(y))) + 2*re(x)*im(x)*im(x/sqrt(y + tan(y))) + re(x/sqrt(y + tan(y)))*im(x)^2 - 2*re(x/sqrt(y + tan(y))))*cos(re(x)^2*im(x/sqrt(y + tan(y))) + 2*re(x)*re(x/sqrt(y + tan(y)))*im(x) - im(x)^2*im(x/sqrt(y + tan(y))) + 2*im(x/sqrt(y + tan(y))))