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y=(-4^sinx)(arctg3x)

Derivada de y=(-4^sinx)(arctg3x)

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

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Solución

Ha introducido [src]
  sin(x)          
-4      *atan(3*x)
$$- 4^{\sin{\left(x \right)}} \operatorname{atan}{\left(3 x \right)}$$
(-4^sin(x))*atan(3*x)
Gráfica
Primera derivada [src]
     sin(x)                                  
  3*4          sin(x)                        
- --------- - 4      *atan(3*x)*cos(x)*log(4)
          2                                  
   1 + 9*x                                   
$$- 4^{\sin{\left(x \right)}} \log{\left(4 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} - \frac{3 \cdot 4^{\sin{\left(x \right)}}}{9 x^{2} + 1}$$
Segunda derivada [src]
 sin(x) /    54*x      /     2                   \                    6*cos(x)*log(4)\
4      *|----------- + \- cos (x)*log(4) + sin(x)/*atan(3*x)*log(4) - ---------------|
        |          2                                                             2   |
        |/       2\                                                       1 + 9*x    |
        \\1 + 9*x /                                                                  /
$$4^{\sin{\left(x \right)}} \left(\frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \left(\sin{\left(x \right)} - \log{\left(4 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(4 \right)} \operatorname{atan}{\left(3 x \right)} - \frac{6 \log{\left(4 \right)} \cos{\left(x \right)}}{9 x^{2} + 1}\right)$$
Tercera derivada [src]
        /     /          2  \                                                                                                                               \
        |     |      36*x   |                                                                                                                               |
        |  54*|-1 + --------|                                                                                                                               |
        |     |            2|     /     2                   \                                                                                               |
 sin(x) |     \     1 + 9*x /   9*\- cos (x)*log(4) + sin(x)/*log(4)   /       2       2                     \                           162*x*cos(x)*log(4)|
4      *|- ------------------ + ------------------------------------ + \1 - cos (x)*log (4) + 3*log(4)*sin(x)/*atan(3*x)*cos(x)*log(4) + -------------------|
        |               2                            2                                                                                                 2    |
        |     /       2\                      1 + 9*x                                                                                        /       2\     |
        \     \1 + 9*x /                                                                                                                     \1 + 9*x /     /
$$4^{\sin{\left(x \right)}} \left(\frac{162 x \log{\left(4 \right)} \cos{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2}} + \left(3 \log{\left(4 \right)} \sin{\left(x \right)} - \log{\left(4 \right)}^{2} \cos^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{9 \left(\sin{\left(x \right)} - \log{\left(4 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(4 \right)}}{9 x^{2} + 1} - \frac{54 \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=(-4^sinx)(arctg3x)