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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Expresiones idénticas
y=th^ dos (x+ tres)/arctansqrtx
y es igual a th al cuadrado (x más 3) dividir por arc tangente de raíz cuadrada de x
y es igual a th en el grado dos (x más tres) dividir por arc tangente de raíz cuadrada de x
y=th^2(x+3)/arctan√x
y=th2(x+3)/arctansqrtx
y=th2x+3/arctansqrtx
y=th²(x+3)/arctansqrtx
y=th en el grado 2(x+3)/arctansqrtx
y=th^2x+3/arctansqrtx
y=th^2(x+3) dividir por arctansqrtx
Expresiones semejantes
y=th^2(x-3)/arctansqrtx

Derivada de la función/ arctan/ sqrtx/ (x+3)/ y=th^2(x+3)/arctansqrtx

Derivada de y=th^2(x+3)/arctansqrtx

Solución

Ha introducido [src]

    2       
tanh (x + 3)
------------
    /  ___\ 
atan\\/ x /

\frac{\tanh^{2}{\left(x + 3 \right)}}{\operatorname{atan}{\left(\sqrt{x} \right)}}

tanh(x + 3)^2/atan(sqrt(x))

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

/          2       \                           2               
\2 - 2*tanh (x + 3)/*tanh(x + 3)           tanh (x + 3)        
-------------------------------- - ----------------------------
              /  ___\                  ___             2/  ___\
          atan\\/ x /              2*\/ x *(1 + x)*atan \\/ x /

\frac{\left(2 - 2 \tanh^{2}{\left(x + 3 \right)}\right) \tanh{\left(x + 3 \right)}}{\operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{\tanh^{2}{\left(x + 3 \right)}}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}^{2}{\left(\sqrt{x} \right)}}

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Segunda derivada [src]

                                                  2        / 1           2                   2          \                                    
                                              tanh (3 + x)*|---- + ------------- + ---------------------|                                    
                                                           | 3/2     ___                         /  ___\|     /         2       \            
  /         2       \ /           2       \                \x      \/ x *(1 + x)   x*(1 + x)*atan\\/ x //   2*\-1 + tanh (3 + x)/*tanh(3 + x)
2*\-1 + tanh (3 + x)/*\-1 + 3*tanh (3 + x)/ + ----------------------------------------------------------- + ---------------------------------
                                                                               /  ___\                            ___             /  ___\    
                                                                 4*(1 + x)*atan\\/ x /                          \/ x *(1 + x)*atan\\/ x /    
---------------------------------------------------------------------------------------------------------------------------------------------
                                                                     /  ___\                                                                 
                                                                 atan\\/ x /

\frac{2 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 1\right) + \frac{\left(\frac{2}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \tanh^{2}{\left(x + 3 \right)}}{4 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \tanh{\left(x + 3 \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}}{\operatorname{atan}{\left(\sqrt{x} \right)}}

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Tercera derivada [src]

 /                                                              2        / 3          4               8                    6                          6                          12          \                                                   /         2       \ / 1           2                   2          \            \ 
 |                                                          tanh (3 + x)*|---- + ------------ + -------------- + ---------------------- + -------------------------- + ----------------------|                                                 3*\-1 + tanh (3 + x)/*|---- + ------------- + ---------------------|*tanh(3 + x)| 
 |                                                                       | 5/2    3/2             ___        2    2             /  ___\    3/2        2     2/  ___\            2     /  ___\|     /         2       \ /           2       \                         | 3/2     ___                         /  ___\|            | 
 |  /         2       \ /           2       \                            \x      x   *(1 + x)   \/ x *(1 + x)    x *(1 + x)*atan\\/ x /   x   *(1 + x) *atan \\/ x /   x*(1 + x) *atan\\/ x //   3*\-1 + tanh (3 + x)/*\-1 + 3*tanh (3 + x)/                         \x      \/ x *(1 + x)   x*(1 + x)*atan\\/ x //            | 
-|8*\-1 + tanh (3 + x)/*\-2 + 3*tanh (3 + x)/*tanh(3 + x) + ---------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------- + --------------------------------------------------------------------------------| 
 |                                                                                                                              /  ___\                                                                     ___             /  ___\                                                       /  ___\                              | 
 \                                                                                                                8*(1 + x)*atan\\/ x /                                                                   \/ x *(1 + x)*atan\\/ x /                                         2*(1 + x)*atan\\/ x /                              / 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                               /  ___\                                                                                                                                                           
                                                                                                                                                           atan\\/ x /

- \frac{8 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 2\right) \tanh{\left(x + 3 \right)} + \frac{3 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(\frac{2}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \tanh{\left(x + 3 \right)}}{2 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\left(\frac{12}{x \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{6}{x^{2} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{8}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{4}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{6}{x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{3}{x^{\frac{5}{2}}}\right) \tanh^{2}{\left(x + 3 \right)}}{8 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{3 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 1\right)}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}}{\operatorname{atan}{\left(\sqrt{x} \right)}}

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Gráfico

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Derivada de y=th^2(x+3)/arctansqrtx

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