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Expresiones idénticas
y=ln^ cuatro (uno -arctg3x)
y es igual a ln en el grado 4(1 menos arctg3x)
y es igual a ln en el grado cuatro (uno menos arctg3x)
y=ln4(1-arctg3x)
y=ln41-arctg3x
y=ln⁴(1-arctg3x)
y=ln^41-arctg3x
Expresiones semejantes
y=ln^4(1+arctg3x)
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ln
ln(x+√(x²+1))
ln(x+1)/x^2
ln(x^1/2)
ln(x+k)
ln(ax)

Derivada de la función/ arctg/ ctg3x/ y=ln^4(1-arctg3x)

Derivada de y=ln^4(1-arctg3x)

Solución

Ha introducido [src]

   4               
log (1 - atan(3*x))

\log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{4}

log(1 - atan(3*x))^4

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

        3                 
 -12*log (1 - atan(3*x))  
--------------------------
                /       2\
(1 - atan(3*x))*\1 + 9*x /

- \frac{12 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{3}}{\left(1 - \operatorname{atan}{\left(3 x \right)}\right) \left(9 x^{2} + 1\right)}

Simplificar

Segunda derivada [src]

      2                /      3          log(1 - atan(3*x))                         \
36*log (1 - atan(3*x))*|-------------- - ------------------ - 6*x*log(1 - atan(3*x))|
                       \-1 + atan(3*x)     -1 + atan(3*x)                           /
-------------------------------------------------------------------------------------
                                       2                                             
                             /       2\                                              
                             \1 + 9*x / *(-1 + atan(3*x))

\frac{36 \left(- 6 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)} - \frac{\log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\operatorname{atan}{\left(3 x \right)} - 1} + \frac{3}{\operatorname{atan}{\left(3 x \right)} - 1}\right) \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(3 x \right)} - 1\right)}

Simplificar

Tercera derivada [src]

    /                                                                                                2                          2    2                                                          2                \                   
    |       2                               6                     9*log(1 - atan(3*x))          2*log (1 - atan(3*x))       72*x *log (1 - atan(3*x))     54*x*log(1 - atan(3*x))       18*x*log (1 - atan(3*x)) |                   
108*|- 2*log (1 - atan(3*x)) + ---------------------------- - ---------------------------- + ---------------------------- + ------------------------- - --------------------------- + ---------------------------|*log(1 - atan(3*x))
    |                          /       2\                 2   /       2\                 2   /       2\                 2                   2           /       2\                    /       2\                 |                   
    \                          \1 + 9*x /*(-1 + atan(3*x))    \1 + 9*x /*(-1 + atan(3*x))    \1 + 9*x /*(-1 + atan(3*x))             1 + 9*x            \1 + 9*x /*(-1 + atan(3*x))   \1 + 9*x /*(-1 + atan(3*x))/                   
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                               2                                                                                                                     
                                                                                                     /       2\                                                                                                                      
                                                                                                     \1 + 9*x / *(-1 + atan(3*x))

\frac{108 \left(\frac{72 x^{2} \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{9 x^{2} + 1} + \frac{18 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)} - \frac{54 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)} - 2 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2} + \frac{2 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}} - \frac{9 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}} + \frac{6}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}}\right) \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(3 x \right)} - 1\right)}

Simplificar

Gráfico

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Expresiones con funciones

Derivada de y=ln^4(1-arctg3x)

Gráfico:

Definida a trozos:

Solución