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x^(sin(pi*x)+1)

Derivada de x^(sin(pi*x)+1)

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

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Solución

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

    Perola derivada

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

  2. Simplificamos:

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


Respuesta:

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

Gráfica
02468-8-6-4-2-1010-500500
Primera derivada [src]
 sin(pi*x) + 1 /sin(pi*x) + 1                      \
x             *|------------- + pi*cos(pi*x)*log(x)|
               \      x                            /
xsin(πx)+1(πlog(x)cos(πx)+sin(πx)+1x)x^{\sin{\left(\pi x \right)} + 1} \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right)
Segunda derivada [src]
               /                                     2                                                        \
 1 + sin(pi*x) |/1 + sin(pi*x)                      \    1 + 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)+1((πlog(x)cos(πx)+sin(πx)+1x)2π2log(x)sin(πx)+2πcos(πx)xsin(πx)+1x2)x^{\sin{\left(\pi x \right)} + 1} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{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)} + 1}{x^{2}}\right)
Tercera derivada [src]
               /                                     3                                                                                                                                                                     2          \
 1 + sin(pi*x) |/1 + sin(pi*x)                      \      /1 + sin(pi*x)                      \ /1 + sin(pi*x)     2                    2*pi*cos(pi*x)\   2*(1 + 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)+1((πlog(x)cos(πx)+sin(πx)+1x)33(πlog(x)cos(πx)+sin(πx)+1x)(π2log(x)sin(πx)2πcos(πx)x+sin(πx)+1x2)π3log(x)cos(πx)3π2sin(πx)x3πcos(πx)x2+2(sin(πx)+1)x3)x^{\sin{\left(\pi x \right)} + 1} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right)^{3} - 3 \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{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)} + 1}{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 \left(\sin{\left(\pi x \right)} + 1\right)}{x^{3}}\right)
Gráfico
Derivada de x^(sin(pi*x)+1)