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y=chxe^-3xsinx+2^2
Derivada de la función/ x+2^2/ xsinx/ e^-3x/ sinx+2/ y=chxe^-3xsinx+2^2

Derivada de y=chxe^-3xsinx+2^2

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

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Solución

Ha introducido [src] 
    x                
----------*sin(x) + 4
    3                
cosh (x*E)
xcosh⁡3(ex)sin⁡(x)+4\frac{x}{\cosh^{3}{\left(e x \right)}} \sin{\left(x \right)} + 4 
(x/cosh(x*E)^3)*sin(x) + 4
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/    1        3*E*x*sinh(x*E)\           x*cos(x) 
|---------- - ---------------|*sin(x) + ----------
|    3               4       |              3     
\cosh (x*E)      cosh (x*E)  /          cosh (x*E)
xcos⁡(x)cosh⁡3(ex)+(−3exsinh⁡(ex)cosh⁡4(ex)+1cosh⁡3(ex))sin⁡(x)\frac{x \cos{\left(x \right)}}{\cosh^{3}{\left(e x \right)}} + \left(- \frac{3 e x \sinh{\left(e x \right)}}{\cosh^{4}{\left(e x \right)}} + \frac{1}{\cosh^{3}{\left(e x \right)}}\right) \sin{\left(x \right)}
Simplificar
Segunda derivada [src] 
                                                /                              2     \                                         
            /     3*E*x*sinh(E*x)\              |      2*sinh(E*x)   4*E*x*sinh (E*x)|          3*E*x*cos(x)*sinh(E*x)         
-x*sin(x) - |-1 + ---------------|*cos(x) - 3*E*|E*x + ----------- - ----------------|*sin(x) - ---------------------- + cos(x)
            \        cosh(E*x)   /              |       cosh(E*x)           2        |                cosh(E*x)                
                                                \                       cosh (E*x)   /                                         
-------------------------------------------------------------------------------------------------------------------------------
                                                               3                                                               
                                                           cosh (E*x)
−xsin⁡(x)−3excos⁡(x)sinh⁡(ex)cosh⁡(ex)−(3exsinh⁡(ex)cosh⁡(ex)−1)cos⁡(x)−3e(−4exsinh⁡2(ex)cosh⁡2(ex)+ex+2sinh⁡(ex)cosh⁡(ex))sin⁡(x)+cos⁡(x)cosh⁡3(ex)\frac{- x \sin{\left(x \right)} - \frac{3 e x \cos{\left(x \right)} \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}} - \left(\frac{3 e x \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}} - 1\right) \cos{\left(x \right)} - 3 e \left(- \frac{4 e x \sinh^{2}{\left(e x \right)}}{\cosh^{2}{\left(e x \right)}} + e x + \frac{2 \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}}\right) \sin{\left(x \right)} + \cos{\left(x \right)}}{\cosh^{3}{\left(e x \right)}}
Simplificar
Tercera derivada [src] 
                                                           /                              2     \                            /           2                                      3     \                                                                      2              2
            /     3*E*x*sinh(E*x)\                         |      2*sinh(E*x)   4*E*x*sinh (E*x)|                      2     |    12*sinh (E*x)   11*E*x*sinh(E*x)   20*E*x*sinh (E*x)|  2          6*E*cos(x)*sinh(E*x)   6*E*x*sin(x)*sinh(E*x)   12*x*sinh (E*x)*cos(x)*e 
-2*sin(x) + |-1 + ---------------|*sin(x) - x*cos(x) - 6*E*|E*x + ----------- - ----------------|*cos(x) - 3*x*cos(x)*e  - 3*|3 - ------------- - ---------------- + -----------------|*e *sin(x) - -------------------- + ---------------------- + -------------------------
            \        cosh(E*x)   /                         |       cosh(E*x)           2        |                            |          2            cosh(E*x)               3        |                  cosh(E*x)               cosh(E*x)                      2            
                                                           \                       cosh (E*x)   /                            \      cosh (E*x)                           cosh (E*x)   /                                                                     cosh (E*x)       
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                                                                                                                                      3                                                                                                                                      
                                                                                                                                  cosh (E*x)
6exsin⁡(x)sinh⁡(ex)cosh⁡(ex)+12xe2cos⁡(x)sinh⁡2(ex)cosh⁡2(ex)−3xe2cos⁡(x)−xcos⁡(x)+(3exsinh⁡(ex)cosh⁡(ex)−1)sin⁡(x)−6e(−4exsinh⁡2(ex)cosh⁡2(ex)+ex+2sinh⁡(ex)cosh⁡(ex))cos⁡(x)−3(20exsinh⁡3(ex)cosh⁡3(ex)−11exsinh⁡(ex)cosh⁡(ex)−12sinh⁡2(ex)cosh⁡2(ex)+3)e2sin⁡(x)−2sin⁡(x)−6ecos⁡(x)sinh⁡(ex)cosh⁡(ex)cosh⁡3(ex)\frac{\frac{6 e x \sin{\left(x \right)} \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}} + \frac{12 x e^{2} \cos{\left(x \right)} \sinh^{2}{\left(e x \right)}}{\cosh^{2}{\left(e x \right)}} - 3 x e^{2} \cos{\left(x \right)} - x \cos{\left(x \right)} + \left(\frac{3 e x \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}} - 1\right) \sin{\left(x \right)} - 6 e \left(- \frac{4 e x \sinh^{2}{\left(e x \right)}}{\cosh^{2}{\left(e x \right)}} + e x + \frac{2 \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}}\right) \cos{\left(x \right)} - 3 \left(\frac{20 e x \sinh^{3}{\left(e x \right)}}{\cosh^{3}{\left(e x \right)}} - \frac{11 e x \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}} - \frac{12 \sinh^{2}{\left(e x \right)}}{\cosh^{2}{\left(e x \right)}} + 3\right) e^{2} \sin{\left(x \right)} - 2 \sin{\left(x \right)} - \frac{6 e \cos{\left(x \right)} \sinh{\left(e x \right)}}{\cosh{\left(e x \right)}}}{\cosh^{3}{\left(e x \right)}}
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Gráfico
Derivada de y=chxe^-3xsinx+2^2
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