Derivada de x^(ln(2x+1))

Ha introducido [src]

 log(2*x + 1)
x

$$x^{\log{\left(2 x + 1 \right)}}$$

x^log(2*x + 1)

Solución detallada

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Perola derivada

$\left(\log{\left(\log{\left(2 x + 1 \right)} \right)} + 1\right) \log{\left(2 x + 1 \right)}^{\log{\left(2 x + 1 \right)}}$
Simplificamos:

$\left(\log{\left(\log{\left(2 x + 1 \right)} \right)} + 1\right) \log{\left(2 x + 1 \right)}^{\log{\left(2 x + 1 \right)}}$

Respuesta:

$\left(\log{\left(\log{\left(2 x + 1 \right)} \right)} + 1\right) \log{\left(2 x + 1 \right)}^{\log{\left(2 x + 1 \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

 log(2*x + 1) /log(2*x + 1)   2*log(x)\
x            *|------------ + --------|
              \     x         2*x + 1 /

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

              /                         3                                                                                                                                    \
 log(1 + 2*x) |/log(1 + 2*x)   2*log(x)\         12             6           /log(1 + 2*x)   2*log(x)\ /log(1 + 2*x)        4         4*log(x) \   2*log(1 + 2*x)   16*log(x) |
x            *||------------ + --------|  - ------------ - ------------ - 3*|------------ + --------|*|------------ - ----------- + ----------| + -------------- + ----------|
              |\     x         1 + 2*x /               2    2               \     x         1 + 2*x / |      2        x*(1 + 2*x)            2|          3                  3|
              \                             x*(1 + 2*x)    x *(1 + 2*x)                               \     x                       (1 + 2*x) /         x          (1 + 2*x) /

$$x^{\log{\left(2 x + 1 \right)}} \left(\left(\frac{2 \log{\left(x \right)}}{2 x + 1} + \frac{\log{\left(2 x + 1 \right)}}{x}\right)^{3} - 3 \left(\frac{2 \log{\left(x \right)}}{2 x + 1} + \frac{\log{\left(2 x + 1 \right)}}{x}\right) \left(\frac{4 \log{\left(x \right)}}{\left(2 x + 1\right)^{2}} - \frac{4}{x \left(2 x + 1\right)} + \frac{\log{\left(2 x + 1 \right)}}{x^{2}}\right) + \frac{16 \log{\left(x \right)}}{\left(2 x + 1\right)^{3}} - \frac{12}{x \left(2 x + 1\right)^{2}} - \frac{6}{x^{2} \left(2 x + 1\right)} + \frac{2 \log{\left(2 x + 1 \right)}}{x^{3}}\right)$$

Simplificar

Gráfico

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Derivada de x^(ln(2x+1))

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