Sr Examen

Derivada de x^sinπx

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

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Definida a trozos:

Solución

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

    Perola derivada

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


Respuesta:

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

Gráfica
02468-8-6-4-2-1010-5050
Primera derivada [src]
 sin(pi*x) /sin(pi*x)                      \
x         *|--------- + pi*cos(pi*x)*log(x)|
           \    x                          /
xsin(πx)(πlog(x)cos(πx)+sin(πx)x)x^{\sin{\left(\pi x \right)}} \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)}}{x}\right)
Segunda derivada [src]
           /                                 2                                                    \
 sin(pi*x) |/sin(pi*x)                      \    sin(pi*x)     2                    2*pi*cos(pi*x)|
x         *||--------- + pi*cos(pi*x)*log(x)|  - --------- - pi *log(x)*sin(pi*x) + --------------|
           |\    x                          /         2                                   x       |
           \                                         x                                            /
xsin(πx)((πlog(x)cos(πx)+sin(πx)x)2π2log(x)sin(πx)+2πcos(πx)xsin(πx)x2)x^{\sin{\left(\pi x \right)}} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)}}{x}\right)^{2} - \pi^{2} \log{\left(x \right)} \sin{\left(\pi x \right)} + \frac{2 \pi \cos{\left(\pi x \right)}}{x} - \frac{\sin{\left(\pi x \right)}}{x^{2}}\right)
Tercera derivada [src]
           /                                 3                                                                                                                                                       2          \
 sin(pi*x) |/sin(pi*x)                      \      /sin(pi*x)                      \ /sin(pi*x)     2                    2*pi*cos(pi*x)\   2*sin(pi*x)     3                    3*pi*cos(pi*x)   3*pi *sin(pi*x)|
x         *||--------- + pi*cos(pi*x)*log(x)|  - 3*|--------- + pi*cos(pi*x)*log(x)|*|--------- + pi *log(x)*sin(pi*x) - --------------| + ----------- - pi *cos(pi*x)*log(x) - -------------- - ---------------|
           |\    x                          /      \    x                          / |     2                                   x       |         3                                     2                x       |
           \                                                                         \    x                                            /        x                                     x                         /
xsin(πx)((πlog(x)cos(πx)+sin(πx)x)33(πlog(x)cos(πx)+sin(πx)x)(π2log(x)sin(πx)2πcos(πx)x+sin(πx)x2)π3log(x)cos(πx)3π2sin(πx)x3πcos(πx)x2+2sin(πx)x3)x^{\sin{\left(\pi x \right)}} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)}}{x}\right)^{3} - 3 \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)}}{x}\right) \left(\pi^{2} \log{\left(x \right)} \sin{\left(\pi x \right)} - \frac{2 \pi \cos{\left(\pi x \right)}}{x} + \frac{\sin{\left(\pi x \right)}}{x^{2}}\right) - \pi^{3} \log{\left(x \right)} \cos{\left(\pi x \right)} - \frac{3 \pi^{2} \sin{\left(\pi x \right)}}{x} - \frac{3 \pi \cos{\left(\pi x \right)}}{x^{2}} + \frac{2 \sin{\left(\pi x \right)}}{x^{3}}\right)
Gráfico
Derivada de x^sinπx