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y=(ch^3)9x*arctg(5x-1)
Derivada de la función/ arctg/ y=(ch^3)9x*arctg(5x-1)

Derivada de y=(ch^3)9x*arctg(5x-1)

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

Ha introducido [src] 
    3                     
cosh (x)*9*x*atan(5*x - 1)
x9cosh⁡3(x)atan⁡(5x−1)x 9 \cosh^{3}{\left(x \right)} \operatorname{atan}{\left(5 x - 1 \right)} 
((cosh(x)^3*9)*x)*atan(5*x - 1)
Gráfica
02468-8-6-4-2-1010-10000000000000001000000000000000
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Primera derivada [src] 
                                                              3    
/    3                 2           \                 45*x*cosh (x) 
\cosh (x)*9 + 27*x*cosh (x)*sinh(x)/*atan(5*x - 1) + --------------
                                                                  2
                                                     1 + (5*x - 1)
45xcosh⁡3(x)(5x−1)2+1+(27xsinh⁡(x)cosh⁡2(x)+9cosh⁡3(x))atan⁡(5x−1)\frac{45 x \cosh^{3}{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1} + \left(27 x \sinh{\left(x \right)} \cosh^{2}{\left(x \right)} + 9 \cosh^{3}{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)}
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Segunda derivada [src] 
  /                                                                                                                 2              \        
  |  /  /    2            2   \                    \                  10*(3*x*sinh(x) + cosh(x))*cosh(x)   50*x*cosh (x)*(-1 + 5*x)|        
9*|3*\x*\cosh (x) + 2*sinh (x)/ + 2*cosh(x)*sinh(x)/*atan(-1 + 5*x) + ---------------------------------- - ------------------------|*cosh(x)
  |                                                                                          2                                 2   |        
  |                                                                            1 + (-1 + 5*x)                 /              2\    |        
  \                                                                                                           \1 + (-1 + 5*x) /    /
9(−50x(5x−1)cosh⁡2(x)((5x−1)2+1)2+3(x(2sinh⁡2(x)+cosh⁡2(x))+2sinh⁡(x)cosh⁡(x))atan⁡(5x−1)+10(3xsinh⁡(x)+cosh⁡(x))cosh⁡(x)(5x−1)2+1)cosh⁡(x)9 \left(- \frac{50 x \left(5 x - 1\right) \cosh^{2}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} + 3 \left(x \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) + 2 \sinh{\left(x \right)} \cosh{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)} + \frac{10 \left(3 x \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cosh{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1}\right) \cosh{\left(x \right)}
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Tercera derivada [src] 
  /                                                                                                                                                                                                                           /                  2 \\
  |                                                                                                                                                                                                                      3    |      4*(-1 + 5*x)  ||
  |                                                                                                                                                                                                            250*x*cosh (x)*|-1 + ---------------||
  |                                                                                                /  /    2            2   \                    \                   2                                                        |                   2||
  |  /  /    2            2   \             /      2            2   \        \                  45*\x*\cosh (x) + 2*sinh (x)/ + 2*cosh(x)*sinh(x)/*cosh(x)   150*cosh (x)*(-1 + 5*x)*(3*x*sinh(x) + cosh(x))                  \     1 + (-1 + 5*x) /|
9*|3*\3*\cosh (x) + 2*sinh (x)/*cosh(x) + x*\2*sinh (x) + 7*cosh (x)/*sinh(x)/*atan(-1 + 5*x) + ---------------------------------------------------------- - ----------------------------------------------- + -------------------------------------|
  |                                                                                                                                2                                                         2                                            2         |
  |                                                                                                                  1 + (-1 + 5*x)                                         /              2\                            /              2\          |
  \                                                                                                                                                                         \1 + (-1 + 5*x) /                            \1 + (-1 + 5*x) /          /
9(250x(4(5x−1)2(5x−1)2+1−1)cosh⁡3(x)((5x−1)2+1)2−150(5x−1)(3xsinh⁡(x)+cosh⁡(x))cosh⁡2(x)((5x−1)2+1)2+45(x(2sinh⁡2(x)+cosh⁡2(x))+2sinh⁡(x)cosh⁡(x))cosh⁡(x)(5x−1)2+1+3(x(2sinh⁡2(x)+7cosh⁡2(x))sinh⁡(x)+3(2sinh⁡2(x)+cosh⁡2(x))cosh⁡(x))atan⁡(5x−1))9 \left(\frac{250 x \left(\frac{4 \left(5 x - 1\right)^{2}}{\left(5 x - 1\right)^{2} + 1} - 1\right) \cosh^{3}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} - \frac{150 \left(5 x - 1\right) \left(3 x \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cosh^{2}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} + \frac{45 \left(x \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) + 2 \sinh{\left(x \right)} \cosh{\left(x \right)}\right) \cosh{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1} + 3 \left(x \left(2 \sinh^{2}{\left(x \right)} + 7 \cosh^{2}{\left(x \right)}\right) \sinh{\left(x \right)} + 3 \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) \cosh{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)}\right)
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Gráfico
Derivada de y=(ch^3)9x*arctg(5x-1)
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