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x*(sin(8x))^(1/4)exp(-x)
Derivada de la función/ exp(-x)/ x*(sin(8x))^(1/4)exp(-x)

Derivada de x*(sin(8x))^(1/4)exp(-x)

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Solución

Ha introducido [src] 
  4 __________  -x
x*\/ sin(8*x) *e
xsin⁡(8x)4e−xx \sqrt[4]{\sin{\left(8 x \right)}} e^{- x} 
(x*sin(8*x)^(1/4))*exp(-x)
Gráfica
02468-8-6-4-2-1010-10000001000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
/4 __________   2*x*cos(8*x)\  -x     4 __________  -x
|\/ sin(8*x)  + ------------|*e   - x*\/ sin(8*x) *e  
|                  3/4      |                         
\               sin   (8*x) /
−xe−xsin⁡(8x)4+(2xcos⁡(8x)sin⁡34(8x)+sin⁡(8x)4)e−x- x e^{- x} \sqrt[4]{\sin{\left(8 x \right)}} + \left(\frac{2 x \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}} + \sqrt[4]{\sin{\left(8 x \right)}}\right) e^{- x}
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Segunda derivada [src] 
/                                        /                      2     \                             \    
|    4 __________     4 __________       |  4 __________   3*cos (8*x)|    4*cos(8*x)   4*x*cos(8*x)|  -x
|- 2*\/ sin(8*x)  + x*\/ sin(8*x)  - 4*x*|4*\/ sin(8*x)  + -----------| + ----------- - ------------|*e  
|                                        |                    7/4     |      3/4           3/4      |    
\                                        \                 sin   (8*x)/   sin   (8*x)   sin   (8*x) /
(−4x(4sin⁡(8x)4+3cos⁡2(8x)sin⁡74(8x))+xsin⁡(8x)4−4xcos⁡(8x)sin⁡34(8x)−2sin⁡(8x)4+4cos⁡(8x)sin⁡34(8x))e−x\left(- 4 x \left(4 \sqrt[4]{\sin{\left(8 x \right)}} + \frac{3 \cos^{2}{\left(8 x \right)}}{\sin^{\frac{7}{4}}{\left(8 x \right)}}\right) + x \sqrt[4]{\sin{\left(8 x \right)}} - \frac{4 x \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}} - 2 \sqrt[4]{\sin{\left(8 x \right)}} + \frac{4 \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}}\right) e^{- x}
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Tercera derivada [src] 
/                                                                                                                           /           2     \         \    
|                                                                                                                           |     21*cos (8*x)|         |    
|                                                                                                                       8*x*|20 + ------------|*cos(8*x)|    
|                                           2                           /                      2     \                      |         2       |         |    
|     4 __________     4 __________   36*cos (8*x)   12*cos(8*x)        |  4 __________   3*cos (8*x)|   6*x*cos(8*x)       \      sin (8*x)  /         |  -x
|- 45*\/ sin(8*x)  - x*\/ sin(8*x)  - ------------ - ----------- + 12*x*|4*\/ sin(8*x)  + -----------| + ------------ + --------------------------------|*e  
|                                        7/4            3/4             |                    7/4     |      3/4                      3/4                |    
\                                     sin   (8*x)    sin   (8*x)        \                 sin   (8*x)/   sin   (8*x)              sin   (8*x)           /
(8x(20+21cos⁡2(8x)sin⁡2(8x))cos⁡(8x)sin⁡34(8x)+12x(4sin⁡(8x)4+3cos⁡2(8x)sin⁡74(8x))−xsin⁡(8x)4+6xcos⁡(8x)sin⁡34(8x)−45sin⁡(8x)4−12cos⁡(8x)sin⁡34(8x)−36cos⁡2(8x)sin⁡74(8x))e−x\left(\frac{8 x \left(20 + \frac{21 \cos^{2}{\left(8 x \right)}}{\sin^{2}{\left(8 x \right)}}\right) \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}} + 12 x \left(4 \sqrt[4]{\sin{\left(8 x \right)}} + \frac{3 \cos^{2}{\left(8 x \right)}}{\sin^{\frac{7}{4}}{\left(8 x \right)}}\right) - x \sqrt[4]{\sin{\left(8 x \right)}} + \frac{6 x \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}} - 45 \sqrt[4]{\sin{\left(8 x \right)}} - \frac{12 \cos{\left(8 x \right)}}{\sin^{\frac{3}{4}}{\left(8 x \right)}} - \frac{36 \cos^{2}{\left(8 x \right)}}{\sin^{\frac{7}{4}}{\left(8 x \right)}}\right) e^{- x}
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Gráfico
Derivada de x*(sin(8x))^(1/4)exp(-x)
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