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Expresiones idénticas
y=ln^ tres (uno +arctg5x)
y es igual a ln al cubo (1 más arctg5x)
y es igual a ln en el grado tres (uno más arctg5x)
y=ln3(1+arctg5x)
y=ln31+arctg5x
y=ln³(1+arctg5x)
y=ln en el grado 3(1+arctg5x)
y=ln^31+arctg5x
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y=ln^3(1-arctg5x)
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ln
ln(x+√(x²+1))
ln(x^1/2)
ln(x+k)
ln(ax)
ln((x^2+a)^0.5)

Derivada de la función/ ctg5x/ arctg/ y=ln^3/ y=ln^3(1+arctg5x)

Derivada de y=ln^3(1+arctg5x)

Solución

Ha introducido [src]

   3               
log (1 + atan(5*x))

\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{3}

log(1 + atan(5*x))^3

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

         2                 
   15*log (1 + atan(5*x))  
---------------------------
/        2\                
\1 + 25*x /*(1 + atan(5*x))

\frac{15 \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}

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Segunda derivada [src]

   /      2         log(1 + atan(5*x))                          \                   
75*|------------- - ------------------ - 10*x*log(1 + atan(5*x))|*log(1 + atan(5*x))
   \1 + atan(5*x)     1 + atan(5*x)                             /                   
------------------------------------------------------------------------------------
                                       2                                            
                            /        2\                                             
                            \1 + 25*x / *(1 + atan(5*x))

\frac{75 \left(- 10 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)} - \frac{\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\operatorname{atan}{\left(5 x \right)} + 1} + \frac{2}{\operatorname{atan}{\left(5 x \right)} + 1}\right) \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}

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Tercera derivada [src]

    /                                                              2                                                           2    2                                                          2                \
    |     2                               1                     log (1 + atan(5*x))            3*log(1 + atan(5*x))       100*x *log (1 + atan(5*x))     30*x*log(1 + atan(5*x))       15*x*log (1 + atan(5*x)) |
750*|- log (1 + atan(5*x)) + ---------------------------- + ---------------------------- - ---------------------------- + -------------------------- - --------------------------- + ---------------------------|
    |                        /        2\                2   /        2\                2   /        2\                2                   2            /        2\                   /        2\                |
    \                        \1 + 25*x /*(1 + atan(5*x))    \1 + 25*x /*(1 + atan(5*x))    \1 + 25*x /*(1 + atan(5*x))            1 + 25*x             \1 + 25*x /*(1 + atan(5*x))   \1 + 25*x /*(1 + atan(5*x))/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                      2                                                                                                          
                                                                                           /        2\                                                                                                           
                                                                                           \1 + 25*x / *(1 + atan(5*x))

\frac{750 \left(\frac{100 x^{2} \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{25 x^{2} + 1} + \frac{15 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)} - \frac{30 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)} - \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2} + \frac{\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}} - \frac{3 \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}} + \frac{1}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}}\right)}{\left(25 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}

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Derivada de y=ln^3(1+arctg5x)

Gráfico:

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Solución