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y=e^xsinhx÷coshx-1^2

Derivada de y=e^xsinhx÷coshx-1^2

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

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Solución

Ha introducido [src]
 x            
E *sinh(x)    
---------- - 1
 cosh(x)      
$$\frac{e^{x} \sinh{\left(x \right)}}{\cosh{\left(x \right)}} - 1$$
(E^x*sinh(x))/cosh(x) - 1
Gráfica
Primera derivada [src]
         x    x               2     x
cosh(x)*e  + e *sinh(x)   sinh (x)*e 
----------------------- - -----------
        cosh(x)                 2    
                            cosh (x) 
$$\frac{e^{x} \sinh{\left(x \right)} + e^{x} \cosh{\left(x \right)}}{\cosh{\left(x \right)}} - \frac{e^{x} \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}}$$
Segunda derivada [src]
/                2            3                                 \   
|            sinh (x)   2*sinh (x)   (cosh(x) + sinh(x))*sinh(x)|  x
|2*cosh(x) - -------- + ---------- - ---------------------------|*e 
|            cosh(x)         2                 cosh(x)          |   
\                        cosh (x)                               /   
--------------------------------------------------------------------
                              cosh(x)                               
$$\frac{\left(- \frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{2 \sinh^{3}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + 2 \cosh{\left(x \right)}\right) e^{x}}{\cosh{\left(x \right)}}$$
Tercera derivada [src]
/           4                                                3            2                                            2                       \   
|     6*sinh (x)   4*sinh(x)   3*(cosh(x) + sinh(x))   4*sinh (x)   7*sinh (x)   4*(cosh(x) + sinh(x))*sinh(x)   2*sinh (x)*(cosh(x) + sinh(x))|  x
|-2 - ---------- - --------- + --------------------- + ---------- + ---------- - ----------------------------- + ------------------------------|*e 
|          4        cosh(x)           cosh(x)               3            2                      2                               3              |   
\      cosh (x)                                         cosh (x)     cosh (x)               cosh (x)                        cosh (x)           /   
$$\left(\frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh^{2}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} - \frac{4 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \frac{3 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\cosh{\left(x \right)}} - \frac{6 \sinh^{4}{\left(x \right)}}{\cosh^{4}{\left(x \right)}} + \frac{4 \sinh^{3}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} + \frac{7 \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - \frac{4 \sinh{\left(x \right)}}{\cosh{\left(x \right)}} - 2\right) e^{x}$$
Gráfico
Derivada de y=e^xsinhx÷coshx-1^2