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y=arctg^34x3^sinx
Derivada de la función/ arctg/ 3^sinx/ y=arctg^34x3^sinx

Derivada de y=arctg^34x3^sinx

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

Ha introducido [src] 
    3       sin(x)
atan (4*x)*3
3sin⁡(x)atan⁡3(4x)3^{\sin{\left(x \right)}} \operatorname{atan}^{3}{\left(4 x \right)} 
atan(4*x)^3*3^sin(x)
Gráfica
02468-8-6-4-2-1010-2525
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Primera derivada [src] 
    sin(x)     2                                        
12*3      *atan (4*x)    sin(x)     3                   
--------------------- + 3      *atan (4*x)*cos(x)*log(3)
              2                                         
      1 + 16*x
3sin⁡(x)log⁡(3)cos⁡(x)atan⁡3(4x)+12⋅3sin⁡(x)atan⁡2(4x)16x2+13^{\sin{\left(x \right)}} \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(4 x \right)} + \frac{12 \cdot 3^{\sin{\left(x \right)}} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1}
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Segunda derivada [src] 
 sin(x) /  96*(-1 + 4*x*atan(4*x))       2      /     2                   \          24*atan(4*x)*cos(x)*log(3)\          
3      *|- ----------------------- - atan (4*x)*\- cos (x)*log(3) + sin(x)/*log(3) + --------------------------|*atan(4*x)
        |                   2                                                                        2         |          
        |        /        2\                                                                 1 + 16*x          |          
        \        \1 + 16*x /                                                                                   /
3sin⁡(x)(−(sin⁡(x)−log⁡(3)cos⁡2(x))log⁡(3)atan⁡2(4x)+24log⁡(3)cos⁡(x)atan⁡(4x)16x2+1−96(4xatan⁡(4x)−1)(16x2+1)2)atan⁡(4x)3^{\sin{\left(x \right)}} \left(- \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(4 x \right)} + \frac{24 \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{96 \left(4 x \operatorname{atan}{\left(4 x \right)} - 1\right)}{\left(16 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(4 x \right)}
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Tercera derivada [src] 
        /    /                                              2     2     \                                                                                                                                                                         \
        |    |    1           2        24*x*atan(4*x)   64*x *atan (4*x)|                                                                                                                                                                         |
        |384*|--------- - atan (4*x) - -------------- + ----------------|                                                                                                                                                                         |
        |    |        2                          2                 2    |                                                                             2      /     2                   \                                                          |
 sin(x) |    \1 + 16*x                   1 + 16*x          1 + 16*x     /       3      /       2       2                     \                 36*atan (4*x)*\- cos (x)*log(3) + sin(x)/*log(3)   288*(-1 + 4*x*atan(4*x))*atan(4*x)*cos(x)*log(3)|
3      *|---------------------------------------------------------------- - atan (4*x)*\1 - cos (x)*log (3) + 3*log(3)*sin(x)/*cos(x)*log(3) - ------------------------------------------------ - ------------------------------------------------|
        |                                     2                                                                                                                           2                                                    2                  |
        |                          /        2\                                                                                                                    1 + 16*x                                          /        2\                   |
        \                          \1 + 16*x /                                                                                                                                                                      \1 + 16*x /                   /
3sin⁡(x)(−(3log⁡(3)sin⁡(x)−log⁡(3)2cos⁡2(x)+1)log⁡(3)cos⁡(x)atan⁡3(4x)−36(sin⁡(x)−log⁡(3)cos⁡2(x))log⁡(3)atan⁡2(4x)16x2+1−288(4xatan⁡(4x)−1)log⁡(3)cos⁡(x)atan⁡(4x)(16x2+1)2+384(64x2atan⁡2(4x)16x2+1−24xatan⁡(4x)16x2+1−atan⁡2(4x)+116x2+1)(16x2+1)2)3^{\sin{\left(x \right)}} \left(- \left(3 \log{\left(3 \right)} \sin{\left(x \right)} - \log{\left(3 \right)}^{2} \cos^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(4 x \right)} - \frac{36 \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{288 \left(4 x \operatorname{atan}{\left(4 x \right)} - 1\right) \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{\left(16 x^{2} + 1\right)^{2}} + \frac{384 \left(\frac{64 x^{2} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{24 x \operatorname{atan}{\left(4 x \right)}}{16 x^{2} + 1} - \operatorname{atan}^{2}{\left(4 x \right)} + \frac{1}{16 x^{2} + 1}\right)}{\left(16 x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=arctg^34x3^sinx
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