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(x*x+1)^lnx
Derivada de la función/ x*x+1/ (x*x+1)^lnx

Derivada de (x*x+1)^lnx

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
         log(x)
(x*x + 1)
(xx+1)log⁡(x)\left(x x + 1\right)^{\log{\left(x \right)}} 
(x*x + 1)^log(x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(log⁡(x))+1)log⁡(x)log⁡(x)\left(\log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\log{\left(x \right)}}

Respuesta:

(log⁡(log⁡(x))+1)log⁡(x)log⁡(x)\left(\log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\log{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-5000050000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         log(x) /log(x*x + 1)   2*x*log(x)\
(x*x + 1)      *|------------ + ----------|
                \     x          x*x + 1  /
(xx+1)log⁡(x)(2xlog⁡(x)xx+1+log⁡(xx+1)x)\left(x x + 1\right)^{\log{\left(x \right)}} \left(\frac{2 x \log{\left(x \right)}}{x x + 1} + \frac{\log{\left(x x + 1 \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
               /                          2                                                \
        log(x) |/   /     2\             \                /     2\                 2       |
/     2\       ||log\1 + x /   2*x*log(x)|      4      log\1 + x /   2*log(x)   4*x *log(x)|
\1 + x /      *||----------- + ----------|  + ------ - ----------- + -------- - -----------|
               ||     x               2  |         2         2             2             2 |
               |\                1 + x   /    1 + x         x         1 + x      /     2\  |
               \                                                                 \1 + x /  /
(x2+1)log⁡(x)(−4x2log⁡(x)(x2+1)2+(2xlog⁡(x)x2+1+log⁡(x2+1)x)2+2log⁡(x)x2+1+4x2+1−log⁡(x2+1)x2)\left(x^{2} + 1\right)^{\log{\left(x \right)}} \left(- \frac{4 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right)^{2} + \frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{4}{x^{2} + 1} - \frac{\log{\left(x^{2} + 1 \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
               /                          3                                                                                                                                          \
        log(x) |/   /     2\             \                  /   /     2\             \ /              /     2\                 2       \        /     2\                     3       |
/     2\       ||log\1 + x /   2*x*log(x)|       12*x       |log\1 + x /   2*x*log(x)| |    4      log\1 + x /   2*log(x)   4*x *log(x)|   2*log\1 + x /   12*x*log(x)   16*x *log(x)|
\1 + x /      *||----------- + ----------|  - --------- - 3*|----------- + ----------|*|- ------ + ----------- - -------- + -----------| + ------------- - ----------- + ------------|
               ||     x               2  |            2     |     x               2  | |       2         2             2             2 |          3                 2             3  |
               |\                1 + x   /    /     2\      \                1 + x   / |  1 + x         x         1 + x      /     2\  |         x          /     2\      /     2\   |
               \                              \1 + x /                                 \                                     \1 + x /  /                    \1 + x /      \1 + x /   /
(x2+1)log⁡(x)(16x3log⁡(x)(x2+1)3−12xlog⁡(x)(x2+1)2−12x(x2+1)2+(2xlog⁡(x)x2+1+log⁡(x2+1)x)3−3(2xlog⁡(x)x2+1+log⁡(x2+1)x)(4x2log⁡(x)(x2+1)2−2log⁡(x)x2+1−4x2+1+log⁡(x2+1)x2)+2log⁡(x2+1)x3)\left(x^{2} + 1\right)^{\log{\left(x \right)}} \left(\frac{16 x^{3} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 x}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right)^{3} - 3 \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right) \left(\frac{4 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}}{x^{2} + 1} - \frac{4}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x^{2}}\right) + \frac{2 \log{\left(x^{2} + 1 \right)}}{x^{3}}\right)
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Gráfico
Derivada de (x*x+1)^lnx
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