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x^log(x+1)
Derivada de la función/ (x+1)/ x^log(x+1)

Derivada de x^log(x+1)

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

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

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

    Perola derivada

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

  2. Simplificamos:

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010500-250
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Trazar el gráfico f'(x)
Primera derivada [src] 
 log(x + 1) /log(x + 1)   log(x)\
x          *|---------- + ------|
            \    x        x + 1 /
xlog⁡(x+1)(log⁡(x)x+1+log⁡(x+1)x)x^{\log{\left(x + 1 \right)}} \left(\frac{\log{\left(x \right)}}{x + 1} + \frac{\log{\left(x + 1 \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
            /                     2                                    \
 log(1 + x) |/log(1 + x)   log(x)\    log(1 + x)    log(x)        2    |
x          *||---------- + ------|  - ---------- - -------- + ---------|
            |\    x        1 + x /         2              2   x*(1 + x)|
            \                             x        (1 + x)             /
xlog⁡(x+1)((log⁡(x)x+1+log⁡(x+1)x)2−log⁡(x)(x+1)2+2x(x+1)−log⁡(x+1)x2)x^{\log{\left(x + 1 \right)}} \left(\left(\frac{\log{\left(x \right)}}{x + 1} + \frac{\log{\left(x + 1 \right)}}{x}\right)^{2} - \frac{\log{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{2}{x \left(x + 1\right)} - \frac{\log{\left(x + 1 \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
            /                     3                                                                                                                  \
 log(1 + x) |/log(1 + x)   log(x)\        3            3          /log(1 + x)   log(x)\ /log(1 + x)    log(x)        2    \   2*log(1 + x)   2*log(x)|
x          *||---------- + ------|  - ---------- - ---------- - 3*|---------- + ------|*|---------- + -------- - ---------| + ------------ + --------|
            |\    x        1 + x /             2    2             \    x        1 + x / |     2              2   x*(1 + x)|         3               3|
            \                         x*(1 + x)    x *(1 + x)                           \    x        (1 + x)             /        x         (1 + x) /
xlog⁡(x+1)((log⁡(x)x+1+log⁡(x+1)x)3−3(log⁡(x)x+1+log⁡(x+1)x)(log⁡(x)(x+1)2−2x(x+1)+log⁡(x+1)x2)+2log⁡(x)(x+1)3−3x(x+1)2−3x2(x+1)+2log⁡(x+1)x3)x^{\log{\left(x + 1 \right)}} \left(\left(\frac{\log{\left(x \right)}}{x + 1} + \frac{\log{\left(x + 1 \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{x + 1} + \frac{\log{\left(x + 1 \right)}}{x}\right) \left(\frac{\log{\left(x \right)}}{\left(x + 1\right)^{2}} - \frac{2}{x \left(x + 1\right)} + \frac{\log{\left(x + 1 \right)}}{x^{2}}\right) + \frac{2 \log{\left(x \right)}}{\left(x + 1\right)^{3}} - \frac{3}{x \left(x + 1\right)^{2}} - \frac{3}{x^{2} \left(x + 1\right)} + \frac{2 \log{\left(x + 1 \right)}}{x^{3}}\right)
Simplificar
Gráfico
Derivada de x^log(x+1)
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