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(x+3)^cot(x)
Derivada de la función/ (x+3)/ cot(x)/ (x+3)^cot(x)

Derivada de (x+3)^cot(x)

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

Gráfico:

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Solución

Ha introducido [src] 
       cot(x)
(x + 3)
(x+3)cot⁡(x)\left(x + 3\right)^{\cot{\left(x \right)}} 
(x + 3)^cot(x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-500000000000000500000000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
       cot(x) /cot(x)   /        2   \           \
(x + 3)      *|------ + \-1 - cot (x)/*log(x + 3)|
              \x + 3                             /
(x+3)cot⁡(x)((−cot⁡2(x)−1)log⁡(x+3)+cot⁡(x)x+3)\left(x + 3\right)^{\cot{\left(x \right)}} \left(\left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(x + 3 \right)} + \frac{\cot{\left(x \right)}}{x + 3}\right)
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Segunda derivada [src] 
              /                                   2                /       2   \                                    \
       cot(x) |//       2   \              cot(x)\     cot(x)    2*\1 + cot (x)/     /       2   \                  |
(3 + x)      *||\1 + cot (x)/*log(3 + x) - ------|  - -------- - --------------- + 2*\1 + cot (x)/*cot(x)*log(3 + x)|
              |\                           3 + x /           2        3 + x                                         |
              \                                       (3 + x)                                                       /
(x+3)cot⁡(x)(((cot⁡2(x)+1)log⁡(x+3)−cot⁡(x)x+3)2+2(cot⁡2(x)+1)log⁡(x+3)cot⁡(x)−2(cot⁡2(x)+1)x+3−cot⁡(x)(x+3)2)\left(x + 3\right)^{\cot{\left(x \right)}} \left(\left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} - \frac{\cot{\left(x \right)}}{x + 3}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} \cot{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x + 3} - \frac{\cot{\left(x \right)}}{\left(x + 3\right)^{2}}\right)
Simplificar
Tercera derivada [src] 
              /                                     3                  2                           /       2   \                                         /             /       2   \                                    \                                          /       2   \       \
       cot(x) |  //       2   \              cot(x)\      /       2   \               2*cot(x)   3*\1 + cot (x)/     //       2   \              cot(x)\ | cot(x)    2*\1 + cot (x)/     /       2   \                  |        2    /       2   \              6*\1 + cot (x)/*cot(x)|
(3 + x)      *|- |\1 + cot (x)/*log(3 + x) - ------|  - 2*\1 + cot (x)/ *log(3 + x) + -------- + --------------- + 3*|\1 + cot (x)/*log(3 + x) - ------|*|-------- + --------------- - 2*\1 + cot (x)/*cot(x)*log(3 + x)| - 4*cot (x)*\1 + cot (x)/*log(3 + x) + ----------------------|
              |  \                           3 + x /                                         3              2        \                           3 + x / |       2        3 + x                                         |                                                3 + x         |
              \                                                                       (3 + x)        (3 + x)                                             \(3 + x)                                                       /                                                              /
(x+3)cot⁡(x)(−((cot⁡2(x)+1)log⁡(x+3)−cot⁡(x)x+3)3+3((cot⁡2(x)+1)log⁡(x+3)−cot⁡(x)x+3)(−2(cot⁡2(x)+1)log⁡(x+3)cot⁡(x)+2(cot⁡2(x)+1)x+3+cot⁡(x)(x+3)2)−2(cot⁡2(x)+1)2log⁡(x+3)−4(cot⁡2(x)+1)log⁡(x+3)cot⁡2(x)+6(cot⁡2(x)+1)cot⁡(x)x+3+3(cot⁡2(x)+1)(x+3)2+2cot⁡(x)(x+3)3)\left(x + 3\right)^{\cot{\left(x \right)}} \left(- \left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} - \frac{\cot{\left(x \right)}}{x + 3}\right)^{3} + 3 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} - \frac{\cot{\left(x \right)}}{x + 3}\right) \left(- 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} \cot{\left(x \right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x + 3} + \frac{\cot{\left(x \right)}}{\left(x + 3\right)^{2}}\right) - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x + 3 \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x + 3 \right)} \cot^{2}{\left(x \right)} + \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x + 3} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x + 3\right)^{2}} + \frac{2 \cot{\left(x \right)}}{\left(x + 3\right)^{3}}\right)
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Gráfico
Derivada de (x+3)^cot(x)
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