Derivada de arctanh(sin2x)

Ha introducido [src]

atanh(sin(2*x))

\operatorname{atanh}{\left(\sin{\left(2 x \right)} \right)}

atanh(sin(2*x))

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

  2*cos(2*x) 
-------------
       2     
1 - sin (2*x)

\frac{2 \cos{\left(2 x \right)}}{1 - \sin^{2}{\left(2 x \right)}}

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Segunda derivada [src]

  /          2       \         
  |     2*cos (2*x)  |         
4*|1 + --------------|*sin(2*x)
  |            2     |         
  \    -1 + sin (2*x)/         
-------------------------------
                 2             
         -1 + sin (2*x)

\frac{4 \left(1 + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} - 1}\right) \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} - 1}

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Tercera derivada [src]

  /          2                2               2         2     \         
  |     6*sin (2*x)      2*cos (2*x)     8*cos (2*x)*sin (2*x)|         
8*|1 - -------------- + -------------- - ---------------------|*cos(2*x)
  |            2                2                          2  |         
  |    -1 + sin (2*x)   -1 + sin (2*x)     /        2     \   |         
  \                                        \-1 + sin (2*x)/   /         
------------------------------------------------------------------------
                                     2                                  
                             -1 + sin (2*x)

\frac{8 \left(1 - \frac{6 \sin^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} - 1} + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} - 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin^{2}{\left(2 x \right)} - 1\right)^{2}}\right) \cos{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} - 1}

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Gráfico

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Derivada de arctanh(sin2x)

Gráfico:

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Solución