Sr Examen

Derivada de lnx^sinx

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   sin(x)   
log      (x)
log(x)sin(x)\log{\left(x \right)}^{\sin{\left(x \right)}}
log(x)^sin(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

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


Respuesta:

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

Gráfica
02468-8-6-4-2-10105-5
Primera derivada [src]
   sin(x)    /                      sin(x) \
log      (x)*|cos(x)*log(log(x)) + --------|
             \                     x*log(x)/
(log(log(x))cos(x)+sin(x)xlog(x))log(x)sin(x)\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}
Segunda derivada [src]
             /                               2                                                         \
   sin(x)    |/                      sin(x) \                           sin(x)      sin(x)     2*cos(x)|
log      (x)*||cos(x)*log(log(x)) + --------|  - log(log(x))*sin(x) - --------- - ---------- + --------|
             |\                     x*log(x)/                          2           2    2      x*log(x)|
             \                                                        x *log(x)   x *log (x)           /
((log(log(x))cos(x)+sin(x)xlog(x))2log(log(x))sin(x)+2cos(x)xlog(x)sin(x)x2log(x)sin(x)x2log(x)2)log(x)sin(x)\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{2} - \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}
Tercera derivada [src]
             /                               3                                                                                                                                                                                            \
   sin(x)    |/                      sin(x) \                           /                      sin(x) \ /                       sin(x)      sin(x)     2*cos(x)\   3*sin(x)    3*cos(x)    3*cos(x)     2*sin(x)    2*sin(x)     3*sin(x) |
log      (x)*||cos(x)*log(log(x)) + --------|  - cos(x)*log(log(x)) - 3*|cos(x)*log(log(x)) + --------|*|log(log(x))*sin(x) + --------- + ---------- - --------| - -------- - --------- - ---------- + --------- + ---------- + ----------|
             |\                     x*log(x)/                           \                     x*log(x)/ |                      2           2    2      x*log(x)|   x*log(x)    2           2    2       3           3    3       3    2   |
             \                                                                                          \                     x *log(x)   x *log (x)           /              x *log(x)   x *log (x)   x *log(x)   x *log (x)   x *log (x)/
((log(log(x))cos(x)+sin(x)xlog(x))33(log(log(x))cos(x)+sin(x)xlog(x))(log(log(x))sin(x)2cos(x)xlog(x)+sin(x)x2log(x)+sin(x)x2log(x)2)log(log(x))cos(x)3sin(x)xlog(x)3cos(x)x2log(x)3cos(x)x2log(x)2+2sin(x)x3log(x)+3sin(x)x3log(x)2+2sin(x)x3log(x)3)log(x)sin(x)\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{3} - 3 \left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}
Gráfico
Derivada de lnx^sinx