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Derivada de la función/ y=ctg/ x^x^4/ y=ctgx^x^4

Derivada de y=ctgx^x^4

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
        / 4\
        \x /
(cot(x))
cot⁡x4(x)\cot^{x^{4}}{\left(x \right)} 
cot(x)^(x^4)
Solución detallada

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

    Perola derivada

    (log⁡(x4)+1)∣x∣4x4\left(\log{\left(x^{4} \right)} + 1\right) \left|{x}\right|^{4 x^{4}}

Respuesta:

(log⁡(x4)+1)∣x∣4x4\left(\log{\left(x^{4} \right)} + 1\right) \left|{x}\right|^{4 x^{4}}

Primera derivada [src] 
        / 4\ /                    4 /        2   \\
        \x / |   3               x *\-1 - cot (x)/|
(cot(x))    *|4*x *log(cot(x)) + -----------------|
             \                         cot(x)     /
(x4(−cot⁡2(x)−1)cot⁡(x)+4x3log⁡(cot⁡(x)))cot⁡x4(x)\left(\frac{x^{4} \left(- \cot^{2}{\left(x \right)} - 1\right)}{\cot{\left(x \right)}} + 4 x^{3} \log{\left(\cot{\left(x \right)} \right)}\right) \cot^{x^{4}}{\left(x \right)}
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Segunda derivada [src] 
                /                                                      2                                        2                    \
           / 4\ |                    /                   /       2   \\                          2 /       2   \        /       2   \|
 2         \x / |                  4 |                 x*\1 + cot (x)/|       2 /       2   \   x *\1 + cot (x)/    8*x*\1 + cot (x)/|
x *(cot(x))    *|12*log(cot(x)) + x *|-4*log(cot(x)) + ---------------|  + 2*x *\1 + cot (x)/ - ----------------- - -----------------|
                |                    \                      cot(x)    /                                 2                 cot(x)     |
                \                                                                                    cot (x)                         /
x2(x4(x(cot⁡2(x)+1)cot⁡(x)−4log⁡(cot⁡(x)))2−x2(cot⁡2(x)+1)2cot⁡2(x)+2x2(cot⁡2(x)+1)−8x(cot⁡2(x)+1)cot⁡(x)+12log⁡(cot⁡(x)))cot⁡x4(x)x^{2} \left(x^{4} \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 4 \log{\left(\cot{\left(x \right)} \right)}\right)^{2} - \frac{x^{2} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 2 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right) - \frac{8 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + 12 \log{\left(\cot{\left(x \right)} \right)}\right) \cot^{x^{4}}{\left(x \right)}
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Tercera derivada [src] 
               /                                                      3                                                                 2                                                 3                                           /                                                       2                    \                     2\
          / 4\ |                    /                   /       2   \\                               /       2   \       2 /       2   \                                   3 /       2   \         /                   /       2   \\ |                                        2 /       2   \        /       2   \|      3 /       2   \ |
          \x / |                  8 |                 x*\1 + cot (x)/|        2 /       2   \   36*x*\1 + cot (x)/   12*x *\1 + cot (x)/       3 /       2   \          2*x *\1 + cot (x)/       4 |                 x*\1 + cot (x)/| |                     2 /       2   \   x *\1 + cot (x)/    8*x*\1 + cot (x)/|   4*x *\1 + cot (x)/ |
x*(cot(x))    *|24*log(cot(x)) - x *|-4*log(cot(x)) + ---------------|  + 24*x *\1 + cot (x)/ - ------------------ - -------------------- - 4*x *\1 + cot (x)/*cot(x) - ------------------- + 3*x *|-4*log(cot(x)) + ---------------|*|-12*log(cot(x)) - 2*x *\1 + cot (x)/ + ----------------- + -----------------| + -------------------|
               |                    \                      cot(x)    /                                cot(x)                  2                                                  3                 \                      cot(x)    / |                                               2                 cot(x)     |          cot(x)      |
               \                                                                                                           cot (x)                                            cot (x)                                                 \                                            cot (x)                         /                      /
x(−x8(x(cot⁡2(x)+1)cot⁡(x)−4log⁡(cot⁡(x)))3+3x4(x(cot⁡2(x)+1)cot⁡(x)−4log⁡(cot⁡(x)))(x2(cot⁡2(x)+1)2cot⁡2(x)−2x2(cot⁡2(x)+1)+8x(cot⁡2(x)+1)cot⁡(x)−12log⁡(cot⁡(x)))−2x3(cot⁡2(x)+1)3cot⁡3(x)+4x3(cot⁡2(x)+1)2cot⁡(x)−4x3(cot⁡2(x)+1)cot⁡(x)−12x2(cot⁡2(x)+1)2cot⁡2(x)+24x2(cot⁡2(x)+1)−36x(cot⁡2(x)+1)cot⁡(x)+24log⁡(cot⁡(x)))cot⁡x4(x)x \left(- x^{8} \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 4 \log{\left(\cot{\left(x \right)} \right)}\right)^{3} + 3 x^{4} \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 4 \log{\left(\cot{\left(x \right)} \right)}\right) \left(\frac{x^{2} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} - 2 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{8 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 12 \log{\left(\cot{\left(x \right)} \right)}\right) - \frac{2 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\cot^{3}{\left(x \right)}} + \frac{4 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot{\left(x \right)}} - 4 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \frac{12 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 24 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right) - \frac{36 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + 24 \log{\left(\cot{\left(x \right)} \right)}\right) \cot^{x^{4}}{\left(x \right)}
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