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y=cos3x*e^sinx+lnarctg2x
Derivada de la función/ arctg/ ctg2x/ y=cos/ e^sinx/ cos3x/ y=cos3x*e^sinx+lnarctg2x

Derivada de y=cos3x*e^sinx+lnarctg2x

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

Gráfico:

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Solución

Ha introducido [src] 
          sin(x)                 
cos(3*x)*E       + log(atan(2*x))
esin⁡(x)cos⁡(3x)+log⁡(atan⁡(2x))e^{\sin{\left(x \right)}} \cos{\left(3 x \right)} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)} 
cos(3*x)*E^sin(x) + log(atan(2*x))
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     sin(x)                     2                              sin(x)
- 3*e      *sin(3*x) + -------------------- + cos(x)*cos(3*x)*e      
                       /       2\                                    
                       \1 + 4*x /*atan(2*x)
−3esin⁡(x)sin⁡(3x)+esin⁡(x)cos⁡(x)cos⁡(3x)+2(4x2+1)atan⁡(2x)- 3 e^{\sin{\left(x \right)}} \sin{\left(3 x \right)} + e^{\sin{\left(x \right)}} \cos{\left(x \right)} \cos{\left(3 x \right)} + \frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}
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Segunda derivada [src] 
              sin(x)             4                 2              sin(x)             sin(x)                   16*x                     sin(x)         
- 9*cos(3*x)*e       - ---------------------- + cos (x)*cos(3*x)*e       - cos(3*x)*e      *sin(x) - --------------------- - 6*cos(x)*e      *sin(3*x)
                                 2                                                                             2                                      
                       /       2\      2                                                             /       2\                                       
                       \1 + 4*x / *atan (2*x)                                                        \1 + 4*x / *atan(2*x)
−16x(4x2+1)2atan⁡(2x)−esin⁡(x)sin⁡(x)cos⁡(3x)−6esin⁡(x)sin⁡(3x)cos⁡(x)+esin⁡(x)cos⁡2(x)cos⁡(3x)−9esin⁡(x)cos⁡(3x)−4(4x2+1)2atan⁡2(2x)- \frac{16 x}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - e^{\sin{\left(x \right)}} \sin{\left(x \right)} \cos{\left(3 x \right)} - 6 e^{\sin{\left(x \right)}} \sin{\left(3 x \right)} \cos{\left(x \right)} + e^{\sin{\left(x \right)}} \cos^{2}{\left(x \right)} \cos{\left(3 x \right)} - 9 e^{\sin{\left(x \right)}} \cos{\left(3 x \right)} - \frac{4}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}}
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Tercera derivada [src] 
                                                                                                                                                                                                                                2                                          
            16                      16                 sin(x)               3              sin(x)                       sin(x)        2     sin(x)               sin(x)                            96*x                    256*x                              sin(x)       
- --------------------- + ---------------------- + 27*e      *sin(3*x) + cos (x)*cos(3*x)*e       - 28*cos(x)*cos(3*x)*e       - 9*cos (x)*e      *sin(3*x) + 9*e      *sin(x)*sin(3*x) + ---------------------- + --------------------- - 3*cos(x)*cos(3*x)*e      *sin(x)
            2                       3                                                                                                                                                               3                        3                                             
  /       2\              /       2\      3                                                                                                                                               /       2\      2        /       2\                                              
  \1 + 4*x / *atan(2*x)   \1 + 4*x / *atan (2*x)                                                                                                                                          \1 + 4*x / *atan (2*x)   \1 + 4*x / *atan(2*x)
256x2(4x2+1)3atan⁡(2x)+96x(4x2+1)3atan⁡2(2x)+9esin⁡(x)sin⁡(x)sin⁡(3x)−3esin⁡(x)sin⁡(x)cos⁡(x)cos⁡(3x)−9esin⁡(x)sin⁡(3x)cos⁡2(x)+27esin⁡(x)sin⁡(3x)+esin⁡(x)cos⁡3(x)cos⁡(3x)−28esin⁡(x)cos⁡(x)cos⁡(3x)−16(4x2+1)2atan⁡(2x)+16(4x2+1)3atan⁡3(2x)\frac{256 x^{2}}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}{\left(2 x \right)}} + \frac{96 x}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(2 x \right)}} + 9 e^{\sin{\left(x \right)}} \sin{\left(x \right)} \sin{\left(3 x \right)} - 3 e^{\sin{\left(x \right)}} \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)} - 9 e^{\sin{\left(x \right)}} \sin{\left(3 x \right)} \cos^{2}{\left(x \right)} + 27 e^{\sin{\left(x \right)}} \sin{\left(3 x \right)} + e^{\sin{\left(x \right)}} \cos^{3}{\left(x \right)} \cos{\left(3 x \right)} - 28 e^{\sin{\left(x \right)}} \cos{\left(x \right)} \cos{\left(3 x \right)} - \frac{16}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{16}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(2 x \right)}}
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Gráfico
Derivada de y=cos3x*e^sinx+lnarctg2x
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