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Expresiones idénticas
y=arctg[ln(x+4x^ dos)]
y es igual a arctg[ln(x más 4x al cuadrado )]
y es igual a arctg[ln(x más 4x en el grado dos)]
y=arctg[ln(x+4x2)]
y=arctg[lnx+4x2]
y=arctg[ln(x+4x²)]
y=arctg[ln(x+4x en el grado 2)]
y=arctg[lnx+4x^2]
Expresiones semejantes
y=arctg[ln(x-4x^2)]
Expresiones con funciones
arctg
arctg(x)
arctg^2(3x)
arctg5x
arctgln5x
arctg3
ln
ln(x)/x
ln(e)
ln^2x
ln(1+e^x)
ln(x-3)

Derivada de la función/ arctg/ y=arctg[ln(x+4x^2)]

Derivada de y=arctg[ln(x+4x^2)]

Solución

Ha introducido [src]

    /   /       2\\
atan\log\x + 4*x //

\operatorname{atan}{\left(\log{\left(4 x^{2} + x \right)} \right)}

atan(log(x + 4*x^2))

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

            1 + 8*x            
-------------------------------
/       2/       2\\ /       2\
\1 + log \x + 4*x //*\x + 4*x /

\frac{8 x + 1}{\left(4 x^{2} + x\right) \left(\log{\left(4 x^{2} + x \right)}^{2} + 1\right)}

Simplificar

Segunda derivada [src]

              2                 2                    
     (1 + 8*x)       2*(1 + 8*x) *log(x*(1 + 4*x))   
8 - ----------- - -----------------------------------
    x*(1 + 4*x)     /       2             \          
                  x*\1 + log (x*(1 + 4*x))/*(1 + 4*x)
-----------------------------------------------------
           /       2             \                   
         x*\1 + log (x*(1 + 4*x))/*(1 + 4*x)

\frac{8 - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)} - \frac{2 \left(8 x + 1\right)^{2} \log{\left(x \left(4 x + 1\right) \right)}}{x \left(4 x + 1\right) \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)}}{x \left(4 x + 1\right) \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)}

Simplificar

Tercera derivada [src]

            /                                        2                         2                             2                                     2    2                \
            |       24*log(x*(1 + 4*x))     (1 + 8*x)                 (1 + 8*x)                   3*(1 + 8*x) *log(x*(1 + 4*x))         4*(1 + 8*x) *log (x*(1 + 4*x))   |
2*(1 + 8*x)*|-12 - --------------------- + ----------- - ----------------------------------- + ----------------------------------- + ------------------------------------|
            |             2                x*(1 + 4*x)     /       2             \               /       2             \                                      2          |
            |      1 + log (x*(1 + 4*x))                 x*\1 + log (x*(1 + 4*x))/*(1 + 4*x)   x*\1 + log (x*(1 + 4*x))/*(1 + 4*x)     /       2             \           |
            \                                                                                                                        x*\1 + log (x*(1 + 4*x))/ *(1 + 4*x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                   2 /       2             \          2                                                                   
                                                                  x *\1 + log (x*(1 + 4*x))/*(1 + 4*x)

\frac{2 \left(8 x + 1\right) \left(-12 - \frac{24 \log{\left(x \left(4 x + 1\right) \right)}}{\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1} + \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)} + \frac{3 \left(8 x + 1\right)^{2} \log{\left(x \left(4 x + 1\right) \right)}}{x \left(4 x + 1\right) \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)} - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right) \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)} + \frac{4 \left(8 x + 1\right)^{2} \log{\left(x \left(4 x + 1\right) \right)}^{2}}{x \left(4 x + 1\right) \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)^{2}}\right)}{x^{2} \left(4 x + 1\right)^{2} \left(\log{\left(x \left(4 x + 1\right) \right)}^{2} + 1\right)}

Simplificar

Gráfico

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Derivada de y=arctg[ln(x+4x^2)]

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Solución