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y=ln^3arctg(5^xsin5^x)
Derivada de la función/ xsin5/ arctg/ y=ln^3/ y=ln^3arctg(5^xsin5^x)

Derivada de y=ln^3arctg(5^xsin5^x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   3        / x    x   \
log (x)*atan\5 *sin (5)/
log⁡(x)3atan⁡(5xsin⁡x(5))\log{\left(x \right)}^{3} \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)} 
log(x)^3*atan(5^x*sin(5)^x)
Gráfica
02468-8-6-4-2-1010-5050
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Trazar el gráfico f'(x)
Primera derivada [src] 
   3    / x    x                             x    x          \        2        / x    x   \
log (x)*\5 *sin (5)*(pi*I + log(-sin(5))) + 5 *sin (5)*log(5)/   3*log (x)*atan\5 *sin (5)/
-------------------------------------------------------------- + --------------------------
                           2*x    2*x                                        x             
                      1 + 5   *sin   (5)
(5xlog⁡(5)sin⁡x(5)+5x(log⁡(−sin⁡(5))+iπ)sin⁡x(5))log⁡(x)352xsin⁡2x(5)+1+3log⁡(x)2atan⁡(5xsin⁡x(5))x\frac{\left(5^{x} \log{\left(5 \right)} \sin^{x}{\left(5 \right)} + 5^{x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \sin^{x}{\left(5 \right)}\right) \log{\left(x \right)}^{3}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{3 \log{\left(x \right)}^{2} \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x}
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Segunda derivada [src] 
/                                                        /                                                                       2*x                               2    2*x   \                                                     \       
|                                      x    2       x    |                     2      2                                       2*5   *(pi*I + log(5) + log(-sin(5))) *sin   (5)|                                                     |       
|                                     5 *log (x)*sin (5)*|(pi*I + log(-sin(5)))  + log (5) + 2*(pi*I + log(-sin(5)))*log(5) - ------------------------------------------------|                                                     |       
|                      / x    x   \                      |                                                                                        2*x    2*x                  |      x    x                                         |       
|  3*(-2 + log(x))*atan\5 *sin (5)/                      \                                                                                   1 + 5   *sin   (5)               /   6*5 *sin (5)*(pi*I + log(5) + log(-sin(5)))*log(x)|       
|- -------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------|*log(x)
|                  2                                                                                   2*x    2*x                                                                                 /     2*x    2*x   \              |       
\                 x                                                                               1 + 5   *sin   (5)                                                                            x*\1 + 5   *sin   (5)/              /
(5x(−2⋅52x(log⁡(−sin⁡(5))+log⁡(5)+iπ)2sin⁡2x(5)52xsin⁡2x(5)+1+log⁡(5)2+(log⁡(−sin⁡(5))+iπ)2+2(log⁡(−sin⁡(5))+iπ)log⁡(5))log⁡(x)2sin⁡x(5)52xsin⁡2x(5)+1+6⋅5x(log⁡(−sin⁡(5))+log⁡(5)+iπ)log⁡(x)sin⁡x(5)x(52xsin⁡2x(5)+1)−3(log⁡(x)−2)atan⁡(5xsin⁡x(5))x2)log⁡(x)\left(\frac{5^{x} \left(- \frac{2 \cdot 5^{2 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{2} \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \log{\left(x \right)}^{2} \sin^{x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{6 \cdot 5^{x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \log{\left(x \right)} \sin^{x}{\left(5 \right)}}{x \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} - \frac{3 \left(\log{\left(x \right)} - 2\right) \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x^{2}}\right) \log{\left(x \right)}
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Tercera derivada [src] 
                                                                 /                                                                                                          4*x                               3    4*x         2*x    2*x    /                     2      2                                    \                               \                                                                                                                                                                                                                 
                                               x    3       x    |                     3      3                             2               2                            8*5   *(pi*I + log(5) + log(-sin(5))) *sin   (5)   8*5   *sin   (5)*\(pi*I + log(-sin(5)))  + log (5) + 2*(pi*I + log(-sin(5)))*log(5)/*(pi*I + log(5) + log(-sin(5)))|                        /                                                                       2*x                               2    2*x   \                                                                   
                                              5 *log (x)*sin (5)*|(pi*I + log(-sin(5)))  + log (5) + 3*(pi*I + log(-sin(5))) *log(5) + 3*log (5)*(pi*I + log(-sin(5))) + ------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------|      x    2       x    |                     2      2                                       2*5   *(pi*I + log(5) + log(-sin(5))) *sin   (5)|                                                                   
                                                                 |                                                                                                                                        2                                                                       2*x    2*x                                                   |   9*5 *log (x)*sin (5)*|(pi*I + log(-sin(5)))  + log (5) + 2*(pi*I + log(-sin(5)))*log(5) - ------------------------------------------------|                                                                   
  /       2              \     / x    x   \                      |                                                                                                                    /     2*x    2*x   \                                                                   1 + 5   *sin   (5)                                                |                        |                                                                                        2*x    2*x                  |      x    x                                                       
6*\1 + log (x) - 3*log(x)/*atan\5 *sin (5)/                      \                                                                                                                    \1 + 5   *sin   (5)/                                                                                                                                     /                        \                                                                                   1 + 5   *sin   (5)               /   9*5 *sin (5)*(-2 + log(x))*(pi*I + log(5) + log(-sin(5)))*log(x)
------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------
                      3                                                                                                                                                                    2*x    2*x                                                                                                                                                                                                           /     2*x    2*x   \                                                                                  2 /     2*x    2*x   \                     
                     x                                                                                                                                                                1 + 5   *sin   (5)                                                                                                                                                                                                      x*\1 + 5   *sin   (5)/                                                                                 x *\1 + 5   *sin   (5)/
5x(8⋅54x(log⁡(−sin⁡(5))+log⁡(5)+iπ)3sin⁡4x(5)(52xsin⁡2x(5)+1)2−8⋅52x(log⁡(5)2+(log⁡(−sin⁡(5))+iπ)2+2(log⁡(−sin⁡(5))+iπ)log⁡(5))(log⁡(−sin⁡(5))+log⁡(5)+iπ)sin⁡2x(5)52xsin⁡2x(5)+1+log⁡(5)3+(log⁡(−sin⁡(5))+iπ)3+3(log⁡(−sin⁡(5))+iπ)2log⁡(5)+3(log⁡(−sin⁡(5))+iπ)log⁡(5)2)log⁡(x)3sin⁡x(5)52xsin⁡2x(5)+1+9⋅5x(−2⋅52x(log⁡(−sin⁡(5))+log⁡(5)+iπ)2sin⁡2x(5)52xsin⁡2x(5)+1+log⁡(5)2+(log⁡(−sin⁡(5))+iπ)2+2(log⁡(−sin⁡(5))+iπ)log⁡(5))log⁡(x)2sin⁡x(5)x(52xsin⁡2x(5)+1)−9⋅5x(log⁡(x)−2)(log⁡(−sin⁡(5))+log⁡(5)+iπ)log⁡(x)sin⁡x(5)x2(52xsin⁡2x(5)+1)+6(log⁡(x)2−3log⁡(x)+1)atan⁡(5xsin⁡x(5))x3\frac{5^{x} \left(\frac{8 \cdot 5^{4 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{3} \sin^{4 x}{\left(5 \right)}}{\left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)^{2}} - \frac{8 \cdot 5^{2 x} \left(\log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{3} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{3} + 3 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} \log{\left(5 \right)} + 3 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}^{2}\right) \log{\left(x \right)}^{3} \sin^{x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{9 \cdot 5^{x} \left(- \frac{2 \cdot 5^{2 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{2} \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \log{\left(x \right)}^{2} \sin^{x}{\left(5 \right)}}{x \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} - \frac{9 \cdot 5^{x} \left(\log{\left(x \right)} - 2\right) \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \log{\left(x \right)} \sin^{x}{\left(5 \right)}}{x^{2} \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} + \frac{6 \left(\log{\left(x \right)}^{2} - 3 \log{\left(x \right)} + 1\right) \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x^{3}}
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Gráfico
Derivada de y=ln^3arctg(5^xsin5^x)
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