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y=(x^3+4)^ctg(2x)
Derivada de la función/ x^3+4/ tg(2x)/ y=(x^3+4)^ctg(2x)

Derivada de y=(x^3+4)^ctg(2x)

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

Gráfico:

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Solución

Ha introducido [src] 
        cot(2*x)
/ 3    \        
\x  + 4/
(x3+4)cot⁡(2x)\left(x^{3} + 4\right)^{\cot{\left(2 x \right)}} 
(x^3 + 4)^cot(2*x)
Solución detallada

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

    Perola derivada

    (log⁡(cot⁡(2x))+1)cot⁡cot⁡(2x)(2x)\left(\log{\left(\cot{\left(2 x \right)} \right)} + 1\right) \cot^{\cot{\left(2 x \right)}}{\left(2 x \right)}

Respuesta:

(log⁡(cot⁡(2x))+1)cot⁡cot⁡(2x)(2x)\left(\log{\left(\cot{\left(2 x \right)} \right)} + 1\right) \cot^{\cot{\left(2 x \right)}}{\left(2 x \right)}

Gráfica
02468-8-6-4-2-1010-3e323e32
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        cot(2*x) /                                    2         \
/ 3    \         |/          2     \    / 3    \   3*x *cot(2*x)|
\x  + 4/        *|\-2 - 2*cot (2*x)/*log\x  + 4/ + -------------|
                 |                                      3       |
                 \                                     x  + 4   /
(x3+4)cot⁡(2x)(3x2cot⁡(2x)x3+4+(−2cot⁡2(2x)−2)log⁡(x3+4))\left(x^{3} + 4\right)^{\cot{\left(2 x \right)}} \left(\frac{3 x^{2} \cot{\left(2 x \right)}}{x^{3} + 4} + \left(- 2 \cot^{2}{\left(2 x \right)} - 2\right) \log{\left(x^{3} + 4 \right)}\right)
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Segunda derivada [src] 
                 /                                                 2                                                                                                \
        cot(2*x) |/                                     2         \        2 /       2     \      4                                                                 |
/     3\         ||    /       2     \    /     3\   3*x *cot(2*x)|    12*x *\1 + cot (2*x)/   9*x *cot(2*x)   6*x*cot(2*x)     /       2     \             /     3\|
\4 + x /        *||- 2*\1 + cot (2*x)/*log\4 + x / + -------------|  - --------------------- - ------------- + ------------ + 8*\1 + cot (2*x)/*cot(2*x)*log\4 + x /|
                 ||                                           3   |                 3                    2             3                                            |
                 |\                                      4 + x    /            4 + x             /     3\         4 + x                                             |
                 \                                                                               \4 + x /                                                           /
(x3+4)cot⁡(2x)(−9x4cot⁡(2x)(x3+4)2−12x2(cot⁡2(2x)+1)x3+4+6xcot⁡(2x)x3+4+(3x2cot⁡(2x)x3+4−2(cot⁡2(2x)+1)log⁡(x3+4))2+8(cot⁡2(2x)+1)log⁡(x3+4)cot⁡(2x))\left(x^{3} + 4\right)^{\cot{\left(2 x \right)}} \left(- \frac{9 x^{4} \cot{\left(2 x \right)}}{\left(x^{3} + 4\right)^{2}} - \frac{12 x^{2} \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 4} + \frac{6 x \cot{\left(2 x \right)}}{x^{3} + 4} + \left(\frac{3 x^{2} \cot{\left(2 x \right)}}{x^{3} + 4} - 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{2} + 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \cot{\left(2 x \right)}\right)
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Tercera derivada [src] 
                 /                                                 3                                                                                                                                                                                                                                                                                                                                                                    \
        cot(2*x) |/                                     2         \                      2                 /                                     2         \ /                                                             4                2 /       2     \\                    3                 /       2     \                                                  4 /       2     \       6                2 /       2     \         |
/     3\         ||    /       2     \    /     3\   3*x *cot(2*x)|       /       2     \     /     3\     |    /       2     \    /     3\   3*x *cot(2*x)| |    /       2     \             /     3\   6*x*cot(2*x)   9*x *cot(2*x)   12*x *\1 + cot (2*x)/|   6*cot(2*x)   54*x *cot(2*x)   36*x*\1 + cot (2*x)/         2      /       2     \    /     3\   54*x *\1 + cot (2*x)/   54*x *cot(2*x)   72*x *\1 + cot (2*x)/*cot(2*x)|
\4 + x /        *||- 2*\1 + cot (2*x)/*log\4 + x / + -------------|  - 16*\1 + cot (2*x)/ *log\4 + x / - 3*|- 2*\1 + cot (2*x)/*log\4 + x / + -------------|*|- 8*\1 + cot (2*x)/*cot(2*x)*log\4 + x / - ------------ + ------------- + ---------------------| + ---------- - -------------- - -------------------- - 32*cot (2*x)*\1 + cot (2*x)/*log\4 + x / + --------------------- + -------------- + ------------------------------|
                 ||                                           3   |                                        |                                           3   | |                                                   3                2                  3       |          3               2                  3                                                                   2                   3                       3            |
                 |\                                      4 + x    /                                        \                                      4 + x    / |                                              4 + x         /     3\              4 + x        |     4 + x        /     3\              4 + x                                                            /     3\            /     3\                   4 + x             |
                 \                                                                                                                                           \                                                            \4 + x /                           /                  \4 + x /                                                                               \4 + x /            \4 + x /                                     /
(x3+4)cot⁡(2x)(54x6cot⁡(2x)(x3+4)3+54x4(cot⁡2(2x)+1)(x3+4)2−54x3cot⁡(2x)(x3+4)2+72x2(cot⁡2(2x)+1)cot⁡(2x)x3+4−36x(cot⁡2(2x)+1)x3+4+(3x2cot⁡(2x)x3+4−2(cot⁡2(2x)+1)log⁡(x3+4))3−3(3x2cot⁡(2x)x3+4−2(cot⁡2(2x)+1)log⁡(x3+4))(9x4cot⁡(2x)(x3+4)2+12x2(cot⁡2(2x)+1)x3+4−6xcot⁡(2x)x3+4−8(cot⁡2(2x)+1)log⁡(x3+4)cot⁡(2x))−16(cot⁡2(2x)+1)2log⁡(x3+4)−32(cot⁡2(2x)+1)log⁡(x3+4)cot⁡2(2x)+6cot⁡(2x)x3+4)\left(x^{3} + 4\right)^{\cot{\left(2 x \right)}} \left(\frac{54 x^{6} \cot{\left(2 x \right)}}{\left(x^{3} + 4\right)^{3}} + \frac{54 x^{4} \left(\cot^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} + 4\right)^{2}} - \frac{54 x^{3} \cot{\left(2 x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{72 x^{2} \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}}{x^{3} + 4} - \frac{36 x \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 4} + \left(\frac{3 x^{2} \cot{\left(2 x \right)}}{x^{3} + 4} - 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{3} - 3 \left(\frac{3 x^{2} \cot{\left(2 x \right)}}{x^{3} + 4} - 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right) \left(\frac{9 x^{4} \cot{\left(2 x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{12 x^{2} \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 4} - \frac{6 x \cot{\left(2 x \right)}}{x^{3} + 4} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \cot{\left(2 x \right)}\right) - 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} + 4 \right)} - 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \cot^{2}{\left(2 x \right)} + \frac{6 \cot{\left(2 x \right)}}{x^{3} + 4}\right)
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Gráfico
Derivada de y=(x^3+4)^ctg(2x)
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