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x^x*arctg(7x)
Derivada de la función/ arctg/ tg(7x)/ x^x*arctg(7x)

Derivada de x^x*arctg(7x)

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

Gráfico:

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Solución

Ha introducido [src] 
 x          
x *atan(7*x)
xxatan⁡(7x)x^{x} \operatorname{atan}{\left(7 x \right)} 
x^x*atan(7*x)
Gráfica
02468-8-6-4-2-1010-50000000000100000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
      x                              
   7*x       x                       
--------- + x *(1 + log(x))*atan(7*x)
        2                            
1 + 49*x
xx(log⁡(x)+1)atan⁡(7x)+7xx49x2+1x^{x} \left(\log{\left(x \right)} + 1\right) \operatorname{atan}{\left(7 x \right)} + \frac{7 x^{x}}{49 x^{2} + 1}
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Segunda derivada [src] 
 x //1               2\                686*x       14*(1 + log(x))\
x *||- + (1 + log(x)) |*atan(7*x) - ------------ + ---------------|
   |\x                /                        2              2   |
   |                                /        2\       1 + 49*x    |
   \                                \1 + 49*x /                   /
xx(−686x(49x2+1)2+((log⁡(x)+1)2+1x)atan⁡(7x)+14(log⁡(x)+1)49x2+1)x^{x} \left(- \frac{686 x}{\left(49 x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \operatorname{atan}{\left(7 x \right)} + \frac{14 \left(\log{\left(x \right)} + 1\right)}{49 x^{2} + 1}\right)
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Tercera derivada [src] 
   /                                                                               /            2 \                      \
   |                                                                               |       196*x  |                      |
   |                                                     /1               2\   686*|-1 + ---------|                      |
   |                                                  21*|- + (1 + log(x)) |       |             2|                      |
 x |/            3   1    3*(1 + log(x))\                \x                /       \     1 + 49*x /   2058*x*(1 + log(x))|
x *||(1 + log(x))  - -- + --------------|*atan(7*x) + ---------------------- + -------------------- - -------------------|
   ||                 2         x       |                           2                         2                      2   |
   |\                x                  /                   1 + 49*x               /        2\            /        2\    |
   \                                                                               \1 + 49*x /            \1 + 49*x /    /
xx(−2058x(log⁡(x)+1)(49x2+1)2+((log⁡(x)+1)3+3(log⁡(x)+1)x−1x2)atan⁡(7x)+21((log⁡(x)+1)2+1x)49x2+1+686(196x249x2+1−1)(49x2+1)2)x^{x} \left(- \frac{2058 x \left(\log{\left(x \right)} + 1\right)}{\left(49 x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) \operatorname{atan}{\left(7 x \right)} + \frac{21 \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{49 x^{2} + 1} + \frac{686 \left(\frac{196 x^{2}}{49 x^{2} + 1} - 1\right)}{\left(49 x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de x^x*arctg(7x)
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