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y=(cos(2x-1))^x
Derivada de la función/ (2x-1)/ y=(cos(2x-1))^x

Derivada de y=(cos(2x-1))^x

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

Ha introducido [src] 
   x         
cos (2*x - 1)
cos⁡x(2x−1)\cos^{x}{\left(2 x - 1 \right)} 
cos(2*x - 1)^x
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Respuesta:

xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-20000000000000000001000000000000000000
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Primera derivada [src] 
   x          /  2*x*sin(2*x - 1)                    \
cos (2*x - 1)*|- ---------------- + log(cos(2*x - 1))|
              \    cos(2*x - 1)                      /
(−2xsin⁡(2x−1)cos⁡(2x−1)+log⁡(cos⁡(2x−1)))cos⁡x(2x−1)\left(- \frac{2 x \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}} + \log{\left(\cos{\left(2 x - 1 \right)} \right)}\right) \cos^{x}{\left(2 x - 1 \right)}
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Segunda derivada [src] 
               /                                         2                                  2          \
   x           |/                      2*x*sin(-1 + 2*x)\          4*sin(-1 + 2*x)   4*x*sin (-1 + 2*x)|
cos (-1 + 2*x)*||-log(cos(-1 + 2*x)) + -----------------|  - 4*x - --------------- - ------------------|
               |\                        cos(-1 + 2*x)  /           cos(-1 + 2*x)         2            |
               \                                                                       cos (-1 + 2*x)  /
(−4xsin⁡2(2x−1)cos⁡2(2x−1)−4x+(2xsin⁡(2x−1)cos⁡(2x−1)−log⁡(cos⁡(2x−1)))2−4sin⁡(2x−1)cos⁡(2x−1))cos⁡x(2x−1)\left(- \frac{4 x \sin^{2}{\left(2 x - 1 \right)}}{\cos^{2}{\left(2 x - 1 \right)}} - 4 x + \left(\frac{2 x \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}} - \log{\left(\cos{\left(2 x - 1 \right)} \right)}\right)^{2} - \frac{4 \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}}\right) \cos^{x}{\left(2 x - 1 \right)}
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Tercera derivada [src] 
               /                                               3         2                                                          /                         2          \                                3          \
   x           |      /                      2*x*sin(-1 + 2*x)\    12*sin (-1 + 2*x)      /                      2*x*sin(-1 + 2*x)\ |    sin(-1 + 2*x)   x*sin (-1 + 2*x)|   16*x*sin(-1 + 2*x)   16*x*sin (-1 + 2*x)|
cos (-1 + 2*x)*|-12 - |-log(cos(-1 + 2*x)) + -----------------|  - ----------------- + 12*|-log(cos(-1 + 2*x)) + -----------------|*|x + ------------- + ----------------| - ------------------ - -------------------|
               |      \                        cos(-1 + 2*x)  /         2                 \                        cos(-1 + 2*x)  / |    cos(-1 + 2*x)       2           |     cos(-1 + 2*x)            3            |
               \                                                     cos (-1 + 2*x)                                                 \                     cos (-1 + 2*x) /                           cos (-1 + 2*x)  /
(−16xsin⁡3(2x−1)cos⁡3(2x−1)−16xsin⁡(2x−1)cos⁡(2x−1)−(2xsin⁡(2x−1)cos⁡(2x−1)−log⁡(cos⁡(2x−1)))3+12(2xsin⁡(2x−1)cos⁡(2x−1)−log⁡(cos⁡(2x−1)))(xsin⁡2(2x−1)cos⁡2(2x−1)+x+sin⁡(2x−1)cos⁡(2x−1))−12sin⁡2(2x−1)cos⁡2(2x−1)−12)cos⁡x(2x−1)\left(- \frac{16 x \sin^{3}{\left(2 x - 1 \right)}}{\cos^{3}{\left(2 x - 1 \right)}} - \frac{16 x \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}} - \left(\frac{2 x \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}} - \log{\left(\cos{\left(2 x - 1 \right)} \right)}\right)^{3} + 12 \left(\frac{2 x \sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}} - \log{\left(\cos{\left(2 x - 1 \right)} \right)}\right) \left(\frac{x \sin^{2}{\left(2 x - 1 \right)}}{\cos^{2}{\left(2 x - 1 \right)}} + x + \frac{\sin{\left(2 x - 1 \right)}}{\cos{\left(2 x - 1 \right)}}\right) - \frac{12 \sin^{2}{\left(2 x - 1 \right)}}{\cos^{2}{\left(2 x - 1 \right)}} - 12\right) \cos^{x}{\left(2 x - 1 \right)}
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Gráfico
Derivada de y=(cos(2x-1))^x
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