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y=(ch(x))^(3/2)

Derivada de y=(ch(x))^(3/2)

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Solución

Ha introducido [src]
    3/2   
cosh   (x)
$$\cosh^{\frac{3}{2}}{\left(x \right)}$$
cosh(x)^(3/2)
Gráfica
Primera derivada [src]
    _________        
3*\/ cosh(x) *sinh(x)
---------------------
          2          
$$\frac{3 \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{2}$$
Segunda derivada [src]
  /                     2    \
  |      3/2        sinh (x) |
3*|2*cosh   (x) + -----------|
  |                 _________|
  \               \/ cosh(x) /
------------------------------
              4               
$$\frac{3 \left(\frac{\sinh^{2}{\left(x \right)}}{\sqrt{\cosh{\left(x \right)}}} + 2 \cosh^{\frac{3}{2}}{\left(x \right)}\right)}{4}$$
Tercera derivada [src]
  /                      2    \        
  |     _________    sinh (x) |        
3*|10*\/ cosh(x)  - ----------|*sinh(x)
  |                     3/2   |        
  \                 cosh   (x)/        
---------------------------------------
                   8                   
$$\frac{3 \left(- \frac{\sinh^{2}{\left(x \right)}}{\cosh^{\frac{3}{2}}{\left(x \right)}} + 10 \sqrt{\cosh{\left(x \right)}}\right) \sinh{\left(x \right)}}{8}$$
Gráfico
Derivada de y=(ch(x))^(3/2)