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y=ctg^8(ln^2(8x))*5^x^2
Derivada de la función/ y=ctg/ 5^x^2/ y=ctg^8(ln^2(8x))*5^x^2

Derivada de y=ctg^8(ln^2(8x))*5^x^2

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

Gráfico:

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Solución

Ha introducido [src] 
                 / 2\
   8/   2     \  \x /
cot \log (8*x)/*5
5x2cot⁡8(log⁡(8x)2)5^{x^{2}} \cot^{8}{\left(\log{\left(8 x \right)}^{2} \right)} 
cot(log(8*x)^2)^8*5^(x^2)
Gráfica
02468-8-6-4-2-1010-5e845e84
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Primera derivada [src] 
                                       / 2\                                                
     / 2\                              \x /    7/   2     \ /        2/   2     \\         
     \x /    8/   2     \          16*5    *cot \log (8*x)/*\-1 - cot \log (8*x)//*log(8*x)
2*x*5    *cot \log (8*x)/*log(5) + --------------------------------------------------------
                                                              x
2⋅5x2xlog⁡(5)cot⁡8(log⁡(8x)2)+16⋅5x2(−cot⁡2(log⁡(8x)2)−1)log⁡(8x)cot⁡7(log⁡(8x)2)x2 \cdot 5^{x^{2}} x \log{\left(5 \right)} \cot^{8}{\left(\log{\left(8 x \right)}^{2} \right)} + \frac{16 \cdot 5^{x^{2}} \left(- \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 1\right) \log{\left(8 x \right)} \cot^{7}{\left(\log{\left(8 x \right)}^{2} \right)}}{x}
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Segunda derivada [src] 
   / 2\                 /                                             /       2/   2     \\ /     /   2     \      /   2     \                 2/   2     \    2              2      /       2/   2     \\\                                                          \
   \x /    6/   2     \ |   2/   2     \ /       2       \          8*\1 + cot \log (8*x)//*\- cot\log (8*x)/ + cot\log (8*x)/*log(8*x) + 4*cot \log (8*x)/*log (8*x) + 14*log (8*x)*\1 + cot \log (8*x)///      /       2/   2     \\    /   2     \                |
2*5    *cot \log (8*x)/*|cot \log (8*x)/*\1 + 2*x *log(5)/*log(5) + --------------------------------------------------------------------------------------------------------------------------------------- - 32*\1 + cot \log (8*x)//*cot\log (8*x)/*log(5)*log(8*x)|
                        |                                                                                                               2                                                                                                                            |
                        \                                                                                                              x                                                                                                                             /
2⋅5x2((2x2log⁡(5)+1)log⁡(5)cot⁡2(log⁡(8x)2)−32(cot⁡2(log⁡(8x)2)+1)log⁡(5)log⁡(8x)cot⁡(log⁡(8x)2)+8(cot⁡2(log⁡(8x)2)+1)(14(cot⁡2(log⁡(8x)2)+1)log⁡(8x)2+4log⁡(8x)2cot⁡2(log⁡(8x)2)+log⁡(8x)cot⁡(log⁡(8x)2)−cot⁡(log⁡(8x)2))x2)cot⁡6(log⁡(8x)2)2 \cdot 5^{x^{2}} \left(\left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 32 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(5 \right)} \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} + \frac{8 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(14 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} + 4 \log{\left(8 x \right)}^{2} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - \cot{\left(\log{\left(8 x \right)}^{2} \right)}\right)}{x^{2}}\right) \cot^{6}{\left(\log{\left(8 x \right)}^{2} \right)}
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Tercera derivada [src] 
                        /                          /                                                                                                                                                                        2                                                                                                                                                                       \                                                                                                                                                                                                                                                                                            \
   / 2\                 |    /       2/   2     \\ |       2/   2     \         3/   2     \                 2/   2     \                  3/   2     \    2              4/   2     \    3            /       2/   2     \\     3           /       2/   2     \\    /   2     \                  2      /       2/   2     \\    /   2     \          2/   2     \    3      /       2/   2     \\|                                                    /       2/   2     \\ /     /   2     \      /   2     \                 2/   2     \    2              2      /       2/   2     \\\    /   2     \                2/   2     \ /       2/   2     \\ /       2       \                |
   \x /    5/   2     \ |  4*\1 + cot \log (8*x)//*\- 3*cot \log (8*x)/ - 12*cot \log (8*x)/*log(8*x) + 2*cot \log (8*x)/*log(8*x) + 12*cot \log (8*x)/*log (8*x) + 16*cot \log (8*x)/*log (8*x) + 168*\1 + cot \log (8*x)// *log (8*x) - 42*\1 + cot \log (8*x)//*cot\log (8*x)/*log(8*x) + 42*log (8*x)*\1 + cot \log (8*x)//*cot\log (8*x)/ + 176*cot \log (8*x)/*log (8*x)*\1 + cot \log (8*x)///        3/   2     \    2    /       2       \   24*\1 + cot \log (8*x)//*\- cot\log (8*x)/ + cot\log (8*x)/*log(8*x) + 4*cot \log (8*x)/*log (8*x) + 14*log (8*x)*\1 + cot \log (8*x)///*cot\log (8*x)/*log(5)   24*cot \log (8*x)/*\1 + cot \log (8*x)//*\1 + 2*x *log(5)/*log(5)*log(8*x)|
4*5    *cot \log (8*x)/*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + x*cot \log (8*x)/*log (5)*\3 + 2*x *log(5)/ + -------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------|
                        |                                                                                                                                                                                       3                                                                                                                                                                                                                                                                                                                   x                                                                                                                      x                                     |
                        \                                                                                                                                                                                      x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /
4⋅5x2(x(2x2log⁡(5)+3)log⁡(5)2cot⁡3(log⁡(8x)2)−24(2x2log⁡(5)+1)(cot⁡2(log⁡(8x)2)+1)log⁡(5)log⁡(8x)cot⁡2(log⁡(8x)2)x+24(cot⁡2(log⁡(8x)2)+1)(14(cot⁡2(log⁡(8x)2)+1)log⁡(8x)2+4log⁡(8x)2cot⁡2(log⁡(8x)2)+log⁡(8x)cot⁡(log⁡(8x)2)−cot⁡(log⁡(8x)2))log⁡(5)cot⁡(log⁡(8x)2)x−4(cot⁡2(log⁡(8x)2)+1)(168(cot⁡2(log⁡(8x)2)+1)2log⁡(8x)3+176(cot⁡2(log⁡(8x)2)+1)log⁡(8x)3cot⁡2(log⁡(8x)2)+42(cot⁡2(log⁡(8x)2)+1)log⁡(8x)2cot⁡(log⁡(8x)2)−42(cot⁡2(log⁡(8x)2)+1)log⁡(8x)cot⁡(log⁡(8x)2)+16log⁡(8x)3cot⁡4(log⁡(8x)2)+12log⁡(8x)2cot⁡3(log⁡(8x)2)−12log⁡(8x)cot⁡3(log⁡(8x)2)+2log⁡(8x)cot⁡2(log⁡(8x)2)−3cot⁡2(log⁡(8x)2))x3)cot⁡5(log⁡(8x)2)4 \cdot 5^{x^{2}} \left(x \left(2 x^{2} \log{\left(5 \right)} + 3\right) \log{\left(5 \right)}^{2} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} - \frac{24 \left(2 x^{2} \log{\left(5 \right)} + 1\right) \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(5 \right)} \log{\left(8 x \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)}}{x} + \frac{24 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(14 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} + 4 \log{\left(8 x \right)}^{2} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - \cot{\left(\log{\left(8 x \right)}^{2} \right)}\right) \log{\left(5 \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)}}{x} - \frac{4 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(168 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right)^{2} \log{\left(8 x \right)}^{3} + 176 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{3} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 42 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - 42 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} + 16 \log{\left(8 x \right)}^{3} \cot^{4}{\left(\log{\left(8 x \right)}^{2} \right)} + 12 \log{\left(8 x \right)}^{2} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} - 12 \log{\left(8 x \right)} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} + 2 \log{\left(8 x \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 3 \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)}\right)}{x^{3}}\right) \cot^{5}{\left(\log{\left(8 x \right)}^{2} \right)}
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Gráfico
Derivada de y=ctg^8(ln^2(8x))*5^x^2
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