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Derivada de:
Derivada de e^x+x^2
Derivada de -e^x
Derivada de x^2sinx
Derivada de x^(1/3)/(3*x+2)
Expresiones idénticas
y=((ch(x))^(tres / dos))/arctg5x
y es igual a ((ch(x)) en el grado (3 dividir por 2)) dividir por arctg5x
y es igual a ((ch(x)) en el grado (tres dividir por dos)) dividir por arctg5x
y=((ch(x))(3/2))/arctg5x
y=chx3/2/arctg5x
y=chx^3/2/arctg5x
y=((ch(x))^(3 dividir por 2)) dividir por arctg5x

Derivada de la función/ arctg/ ctg5x/ ch(x)/ y=((ch(x))^(3/2))/arctg5x

Derivada de y=((ch(x))^(3/2))/arctg5x

Solución

Ha introducido [src]

    3/2   
cosh   (x)
----------
atan(5*x)

\frac{\cosh^{\frac{3}{2}}{\left(x \right)}}{\operatorname{atan}{\left(5 x \right)}}

cosh(x)^(3/2)/atan(5*x)

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

             3/2               _________        
       5*cosh   (x)        3*\/ cosh(x) *sinh(x)
- ---------------------- + ---------------------
  /        2\     2             2*atan(5*x)     
  \1 + 25*x /*atan (5*x)

\frac{3 \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{2 \operatorname{atan}{\left(5 x \right)}} - \frac{5 \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right) \operatorname{atan}^{2}{\left(5 x \right)}}

Simplificar

Segunda derivada [src]

                                                               3/2    /    1          \
      3/2              2            _________           50*cosh   (x)*|--------- + 5*x|
3*cosh   (x)     3*sinh (x)    15*\/ cosh(x) *sinh(x)                 \atan(5*x)      /
------------ + ------------- - ---------------------- + -------------------------------
     2             _________   /        2\                              2              
               4*\/ cosh(x)    \1 + 25*x /*atan(5*x)         /        2\               
                                                             \1 + 25*x / *atan(5*x)    
---------------------------------------------------------------------------------------
                                       atan(5*x)

\frac{\frac{50 \left(5 x + \frac{1}{\operatorname{atan}{\left(5 x \right)}}\right) \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}} + \frac{3 \sinh^{2}{\left(x \right)}}{4 \sqrt{\cosh{\left(x \right)}}} + \frac{3 \cosh^{\frac{3}{2}}{\left(x \right)}}{2} - \frac{15 \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{\left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}}}{\operatorname{atan}{\left(5 x \right)}}

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Tercera derivada [src]

    /                        2    \              /                     2    \                  /                                     2                         \                                            
    |       _________    sinh (x) |              |      3/2        sinh (x) |           3/2    |               3                100*x              30*x        |                                            
  3*|- 10*\/ cosh(x)  + ----------|*sinh(x)   45*|2*cosh   (x) + -----------|   250*cosh   (x)*|-1 + ---------------------- + --------- + ---------------------|         _________ /    1          \        
    |                       3/2   |              |                 _________|                  |     /        2\     2                2   /        2\          |   225*\/ cosh(x) *|--------- + 5*x|*sinh(x)
    \                   cosh   (x)/              \               \/ cosh(x) /                  \     \1 + 25*x /*atan (5*x)   1 + 25*x    \1 + 25*x /*atan(5*x)/                   \atan(5*x)      /        
- ----------------------------------------- - ------------------------------- - -------------------------------------------------------------------------------- + -----------------------------------------
                      8                             /        2\                                                         2                                                               2                   
                                                  4*\1 + 25*x /*atan(5*x)                                    /        2\                                                     /        2\                    
                                                                                                             \1 + 25*x / *atan(5*x)                                          \1 + 25*x / *atan(5*x)         
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 atan(5*x)

\frac{\frac{225 \left(5 x + \frac{1}{\operatorname{atan}{\left(5 x \right)}}\right) \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}} - \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} - \frac{45 \left(\frac{\sinh^{2}{\left(x \right)}}{\sqrt{\cosh{\left(x \right)}}} + 2 \cosh^{\frac{3}{2}}{\left(x \right)}\right)}{4 \left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}} - \frac{250 \left(\frac{100 x^{2}}{25 x^{2} + 1} + \frac{30 x}{\left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}} - 1 + \frac{3}{\left(25 x^{2} + 1\right) \operatorname{atan}^{2}{\left(5 x \right)}}\right) \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}}}{\operatorname{atan}{\left(5 x \right)}}

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Gráfico

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Expresiones idénticas

Derivada de y=((ch(x))^(3/2))/arctg5x

Gráfico:

Definida a trozos:

Solución