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Derivada de la función/ y=x*arctg(*chx)+(*chx)ln*chx

Derivada de y=x*arctg(*chx)+(*chx)ln*chx

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

Gráfico:

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Solución

Ha introducido [src] 
x*atan(cosh(x)) + cosh(x)*log(c)*h*x
xhlog⁡(c)cosh⁡(x)+xatan⁡(cosh⁡(x))x h \log{\left(c \right)} \cosh{\left(x \right)} + x \operatorname{atan}{\left(\cosh{\left(x \right)} \right)} 
x*atan(cosh(x)) + ((cosh(x)*log(c))*h)*x
Primera derivada [src] 
                    x*sinh(x)                                       
cosh(x)*log(c)*h + ------------ + h*x*log(c)*sinh(x) + atan(cosh(x))
                           2                                        
                   1 + cosh (x)
hxlog⁡(c)sinh⁡(x)+hlog⁡(c)cosh⁡(x)+xsinh⁡(x)cosh⁡2(x)+1+atan⁡(cosh⁡(x))h x \log{\left(c \right)} \sinh{\left(x \right)} + h \log{\left(c \right)} \cosh{\left(x \right)} + \frac{x \sinh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1} + \operatorname{atan}{\left(\cosh{\left(x \right)} \right)}
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Segunda derivada [src] 
                                                                                2           
 2*sinh(x)      x*cosh(x)                                               2*x*sinh (x)*cosh(x)
------------ + ------------ + 2*h*log(c)*sinh(x) + h*x*cosh(x)*log(c) - --------------------
        2              2                                                                2   
1 + cosh (x)   1 + cosh (x)                                               /        2   \    
                                                                          \1 + cosh (x)/
hxlog⁡(c)cosh⁡(x)+2hlog⁡(c)sinh⁡(x)+xcosh⁡(x)cosh⁡2(x)+1−2xsinh⁡2(x)cosh⁡(x)(cosh⁡2(x)+1)2+2sinh⁡(x)cosh⁡2(x)+1h x \log{\left(c \right)} \cosh{\left(x \right)} + 2 h \log{\left(c \right)} \sinh{\left(x \right)} + \frac{x \cosh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1} - \frac{2 x \sinh^{2}{\left(x \right)} \cosh{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{2 \sinh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1}
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Tercera derivada [src] 
                                    2                        3                                                         2                      2        3   
 3*cosh(x)      x*sinh(x)     6*sinh (x)*cosh(x)     2*x*sinh (x)                                              6*x*cosh (x)*sinh(x)   8*x*cosh (x)*sinh (x)
------------ + ------------ - ------------------ - --------------- + 3*h*cosh(x)*log(c) + h*x*log(c)*sinh(x) - -------------------- + ---------------------
        2              2                     2                   2                                                             2                       3   
1 + cosh (x)   1 + cosh (x)    /        2   \      /        2   \                                                /        2   \          /        2   \    
                               \1 + cosh (x)/      \1 + cosh (x)/                                                \1 + cosh (x)/          \1 + cosh (x)/
hxlog⁡(c)sinh⁡(x)+3hlog⁡(c)cosh⁡(x)+xsinh⁡(x)cosh⁡2(x)+1−2xsinh⁡3(x)(cosh⁡2(x)+1)2−6xsinh⁡(x)cosh⁡2(x)(cosh⁡2(x)+1)2+8xsinh⁡3(x)cosh⁡2(x)(cosh⁡2(x)+1)3+3cosh⁡(x)cosh⁡2(x)+1−6sinh⁡2(x)cosh⁡(x)(cosh⁡2(x)+1)2h x \log{\left(c \right)} \sinh{\left(x \right)} + 3 h \log{\left(c \right)} \cosh{\left(x \right)} + \frac{x \sinh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1} - \frac{2 x \sinh^{3}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 x \sinh{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{8 x \sinh^{3}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{3}} + \frac{3 \cosh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1} - \frac{6 \sinh^{2}{\left(x \right)} \cosh{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}}
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