Derivada de y=2^x×arctg3x

Ha introducido [src]

 x          
2 *atan(3*x)

2^{x} \operatorname{atan}{\left(3 x \right)}

2^x*atan(3*x)

Gráfica

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Primera derivada [src]

     x                        
  3*2       x                 
-------- + 2 *atan(3*x)*log(2)
       2                      
1 + 9*x

2^{x} \log{\left(2 \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3 \cdot 2^{x}}{9 x^{2} + 1}

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Segunda derivada [src]

 x /   2                    54*x      6*log(2)\
2 *|log (2)*atan(3*x) - ----------- + --------|
   |                              2          2|
   |                    /       2\    1 + 9*x |
   \                    \1 + 9*x /            /

2^{x} \left(- \frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{2} \operatorname{atan}{\left(3 x \right)} + \frac{6 \log{\left(2 \right)}}{9 x^{2} + 1}\right)

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Tercera derivada [src]

   /                                   /          2  \               \
   |                                   |      36*x   |               |
   |                                54*|-1 + --------|               |
   |                         2         |            2|               |
 x |   3                9*log (2)      \     1 + 9*x /   162*x*log(2)|
2 *|log (2)*atan(3*x) + --------- + ------------------ - ------------|
   |                            2                2                 2 |
   |                     1 + 9*x       /       2\        /       2\  |
   \                                   \1 + 9*x /        \1 + 9*x /  /

2^{x} \left(- \frac{162 x \log{\left(2 \right)}}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{3} \operatorname{atan}{\left(3 x \right)} + \frac{9 \log{\left(2 \right)}^{2}}{9 x^{2} + 1} + \frac{54 \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right)

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Gráfico

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Derivada de y=2^x×arctg3x

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