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x^(sin(pi*x)+1)
Derivada de la función/ sin(pi*x)/ x^(sin(pi*x)+1)

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

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

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
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Trazar el gráfico f'(x)
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)
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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)2−π2log⁡(x)sin⁡(πx)+2πcos⁡(πx)x−sin⁡(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)
Simplificar
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)3−3(πlog⁡(x)cos⁡(πx)+sin⁡(πx)+1x)(π2log⁡(x)sin⁡(πx)−2πcos⁡(πx)x+sin⁡(πx)+1x2)−π3log⁡(x)cos⁡(πx)−3π2sin⁡(πx)x−3πcos⁡(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)
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Gráfico
Derivada de x^(sin(pi*x)+1)
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