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y=sin^-1(tanh(x))
Derivada de la función/ y=sin/ tanh(x)/ y=sin^-1(tanh(x))

Derivada de y=sin^-1(tanh(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     1      
------------
sin(tanh(x))
1sin⁡(tanh⁡(x))\frac{1}{\sin{\left(\tanh{\left(x \right)} \right)}} 
1/sin(tanh(x))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /        2   \              
-\1 - tanh (x)/*cos(tanh(x)) 
-----------------------------
           2                 
        sin (tanh(x))
−(1−tanh⁡2(x))cos⁡(tanh⁡(x))sin⁡2(tanh⁡(x))- \frac{\left(1 - \tanh^{2}{\left(x \right)}\right) \cos{\left(\tanh{\left(x \right)} \right)}}{\sin^{2}{\left(\tanh{\left(x \right)} \right)}}
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Segunda derivada [src] 
                /                                              2          /         2   \\
/         2   \ |         2      2*cos(tanh(x))*tanh(x)   2*cos (tanh(x))*\-1 + tanh (x)/|
\-1 + tanh (x)/*|-1 + tanh (x) - ---------------------- + -------------------------------|
                |                     sin(tanh(x))                    2                  |
                \                                                  sin (tanh(x))         /
------------------------------------------------------------------------------------------
                                       sin(tanh(x))
(tanh⁡2(x)−1)(2(tanh⁡2(x)−1)cos⁡2(tanh⁡(x))sin⁡2(tanh⁡(x))+tanh⁡2(x)−1−2cos⁡(tanh⁡(x))tanh⁡(x)sin⁡(tanh⁡(x)))sin⁡(tanh⁡(x))\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(\frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cos^{2}{\left(\tanh{\left(x \right)} \right)}}{\sin^{2}{\left(\tanh{\left(x \right)} \right)}} + \tanh^{2}{\left(x \right)} - 1 - \frac{2 \cos{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sin{\left(\tanh{\left(x \right)} \right)}}\right)}{\sin{\left(\tanh{\left(x \right)} \right)}}
Simplificar
Tercera derivada [src] 
                /                                                                                                          2                                 2                                                         \
                |                                /         2   \                      2                     /         2   \                   /         2   \     3                  2          /         2   \        |
/         2   \ |    /         2   \           2*\-1 + tanh (x)/*cos(tanh(x))   4*tanh (x)*cos(tanh(x))   5*\-1 + tanh (x)/ *cos(tanh(x))   6*\-1 + tanh (x)/ *cos (tanh(x))   12*cos (tanh(x))*\-1 + tanh (x)/*tanh(x)|
\-1 + tanh (x)/*|- 6*\-1 + tanh (x)/*tanh(x) + ------------------------------ + ----------------------- + ------------------------------- + -------------------------------- - ----------------------------------------|
                |                                       sin(tanh(x))                  sin(tanh(x))                  sin(tanh(x))                        3                                      2                       |
                \                                                                                                                                    sin (tanh(x))                          sin (tanh(x))              /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                      sin(tanh(x))
(tanh⁡2(x)−1)(5(tanh⁡2(x)−1)2cos⁡(tanh⁡(x))sin⁡(tanh⁡(x))+6(tanh⁡2(x)−1)2cos⁡3(tanh⁡(x))sin⁡3(tanh⁡(x))−6(tanh⁡2(x)−1)tanh⁡(x)+2(tanh⁡2(x)−1)cos⁡(tanh⁡(x))sin⁡(tanh⁡(x))−12(tanh⁡2(x)−1)cos⁡2(tanh⁡(x))tanh⁡(x)sin⁡2(tanh⁡(x))+4cos⁡(tanh⁡(x))tanh⁡2(x)sin⁡(tanh⁡(x)))sin⁡(tanh⁡(x))\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(\frac{5 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cos{\left(\tanh{\left(x \right)} \right)}}{\sin{\left(\tanh{\left(x \right)} \right)}} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cos^{3}{\left(\tanh{\left(x \right)} \right)}}{\sin^{3}{\left(\tanh{\left(x \right)} \right)}} - 6 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cos{\left(\tanh{\left(x \right)} \right)}}{\sin{\left(\tanh{\left(x \right)} \right)}} - \frac{12 \left(\tanh^{2}{\left(x \right)} - 1\right) \cos^{2}{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sin^{2}{\left(\tanh{\left(x \right)} \right)}} + \frac{4 \cos{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{\sin{\left(\tanh{\left(x \right)} \right)}}\right)}{\sin{\left(\tanh{\left(x \right)} \right)}}
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Gráfico
Derivada de y=sin^-1(tanh(x))
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