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Derivada de la función/ acosx/ x*exp/ exp(-2x)/ x*exp(-2x)(acosx+bsinx)

Derivada de x*exp(-2x)(acosx+bsinx)

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

Gráfico:

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Solución

Ha introducido [src] 
   -2*x                     
x*e    *(acos(x) + b*sin(x))
xe−2x(bsin⁡(x)+acos⁡(x))x e^{- 2 x} \left(b \sin{\left(x \right)} + \operatorname{acos}{\left(x \right)}\right) 
(x*exp(-2*x))*(acos(x) + b*sin(x))
Primera derivada [src] 
/       -2*x    -2*x\                          /       1                \  -2*x
\- 2*x*e     + e    /*(acos(x) + b*sin(x)) + x*|- ----------- + b*cos(x)|*e    
                                               |     ________           |      
                                               |    /      2            |      
                                               \  \/  1 - x             /
x(bcos⁡(x)−11−x2)e−2x+(bsin⁡(x)+acos⁡(x))(−2xe−2x+e−2x)x \left(b \cos{\left(x \right)} - \frac{1}{\sqrt{1 - x^{2}}}\right) e^{- 2 x} + \left(b \sin{\left(x \right)} + \operatorname{acos}{\left(x \right)}\right) \left(- 2 x e^{- 2 x} + e^{- 2 x}\right)
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Segunda derivada [src] 
/    /                x     \                /       1                \                                  \  -2*x
|- x*|b*sin(x) + -----------| - 2*(-1 + 2*x)*|- ----------- + b*cos(x)| + 4*(-1 + x)*(b*sin(x) + acos(x))|*e    
|    |                   3/2|                |     ________           |                                  |      
|    |           /     2\   |                |    /      2            |                                  |      
\    \           \1 - x /   /                \  \/  1 - x             /                                  /
(−x(bsin⁡(x)+x(1−x2)32)+4(x−1)(bsin⁡(x)+acos⁡(x))−2(2x−1)(bcos⁡(x)−11−x2))e−2x\left(- x \left(b \sin{\left(x \right)} + \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) + 4 \left(x - 1\right) \left(b \sin{\left(x \right)} + \operatorname{acos}{\left(x \right)}\right) - 2 \left(2 x - 1\right) \left(b \cos{\left(x \right)} - \frac{1}{\sqrt{1 - x^{2}}}\right)\right) e^{- 2 x}
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Tercera derivada [src] 
/    /                                2   \                                                                                                                     \      
|    |     1                       3*x    |                                                    /                x     \               /       1                \|  -2*x
|- x*|----------- + b*cos(x) + -----------| - 4*(-3 + 2*x)*(b*sin(x) + acos(x)) + 3*(-1 + 2*x)*|b*sin(x) + -----------| + 12*(-1 + x)*|- ----------- + b*cos(x)||*e    
|    |        3/2                      5/2|                                                    |                   3/2|               |     ________           ||      
|    |/     2\                 /     2\   |                                                    |           /     2\   |               |    /      2            ||      
\    \\1 - x /                 \1 - x /   /                                                    \           \1 - x /   /               \  \/  1 - x             //
(−x(bcos⁡(x)+3x2(1−x2)52+1(1−x2)32)+12(x−1)(bcos⁡(x)−11−x2)−4(2x−3)(bsin⁡(x)+acos⁡(x))+3(2x−1)(bsin⁡(x)+x(1−x2)32))e−2x\left(- x \left(b \cos{\left(x \right)} + \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) + 12 \left(x - 1\right) \left(b \cos{\left(x \right)} - \frac{1}{\sqrt{1 - x^{2}}}\right) - 4 \left(2 x - 3\right) \left(b \sin{\left(x \right)} + \operatorname{acos}{\left(x \right)}\right) + 3 \left(2 x - 1\right) \left(b \sin{\left(x \right)} + \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)\right) e^{- 2 x}
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