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Derivada de y=(ln(2*x)+e^(3*x))^(x^2)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
                 / 2\
                 \x /
/            3*x\    
\log(2*x) + E   /    
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}}$$
(log(2*x) + E^(3*x))^(x^2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Primera derivada [src]
                 / 2\ /                            2 /1      3*x\\
                 \x / |                           x *|- + 3*e   ||
/            3*x\     |       /            3*x\      \x         /|
\log(2*x) + E   /    *|2*x*log\log(2*x) + E   / + ---------------|
                      |                                       3*x|
                      \                           log(2*x) + E   /
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(\frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 x \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)$$
Segunda derivada [src]
                      /                                                                      2    2 /  1       3*x\                   2                    \
                 / 2\ |                            /                            /1      3*x\\    x *|- -- + 9*e   |     2 /1      3*x\         /1      3*x\|
                 \x / |                            |                          x*|- + 3*e   ||       |   2         |    x *|- + 3*e   |     4*x*|- + 3*e   ||
/ 3*x           \     |     / 3*x           \    2 |     / 3*x           \      \x         /|       \  x          /       \x         /         \x         /|
\e    + log(2*x)/    *|2*log\e    + log(2*x)/ + x *|2*log\e    + log(2*x)/ + ---------------|  + ------------------ - ------------------ + ----------------|
                      |                            |                          3*x           |      3*x                                 2    3*x            |
                      |                            \                         e    + log(2*x)/     e    + log(2*x)     / 3*x           \    e    + log(2*x) |
                      \                                                                                               \e    + log(2*x)/                    /
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(x^{2} \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)^{2} + \frac{x^{2} \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} - \frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + \frac{4 x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)$$
Tercera derivada [src]
                      /                                                                                                                         2                    3      2 /1      3*x\ /  1       3*x\                                                                                                                                       \
                      |                                                                                                             /1      3*x\       2 /1      3*x\    3*x *|- + 3*e   |*|- -- + 9*e   |                                                                                                                                       |
                      |                                                                                                         6*x*|- + 3*e   |    2*x *|- + 3*e   |         \x         / |   2         |                                                                                                                                       |
                      |                                                 6       3*x    2 /2        3*x\       /  1       3*x\       \x         /         \x         /                      \  x          /                                                                                                                                       |
                      |                                             3   - + 18*e    + x *|-- + 27*e   | + 6*x*|- -- + 9*e   | - ----------------- + ------------------ - ---------------------------------                                                  /                          2 /  1       3*x\                   2                    \|
                 / 2\ |   /                            /1      3*x\\    x                | 3          |       |   2         |     3*x                                2             3*x                           /                            /1      3*x\\ |                         x *|- -- + 9*e   |     2 /1      3*x\         /1      3*x\||
                 \x / |   |                          x*|- + 3*e   ||                     \x           /       \  x          /    e    + log(2*x)    / 3*x           \             e    + log(2*x)                |                          x*|- + 3*e   || |                            |   2         |    x *|- + 3*e   |     4*x*|- + 3*e   |||
/ 3*x           \     | 3 |     / 3*x           \      \x         /|                                                                                \e    + log(2*x)/                                            |     / 3*x           \      \x         /| |     / 3*x           \      \  x          /       \x         /         \x         /||
\e    + log(2*x)/    *|x *|2*log\e    + log(2*x)/ + ---------------|  + ---------------------------------------------------------------------------------------------------------------------------------- + 3*x*|2*log\e    + log(2*x)/ + ---------------|*|2*log\e    + log(2*x)/ + ------------------ - ------------------ + ----------------||
                      |   |                          3*x           |                                                              3*x                                                                            |                          3*x           | |                           3*x                                 2    3*x            ||
                      |   \                         e    + log(2*x)/                                                             e    + log(2*x)                                                                 \                         e    + log(2*x)/ |                          e    + log(2*x)     / 3*x           \    e    + log(2*x) ||
                      \                                                                                                                                                                                                                                     \                                              \e    + log(2*x)/                    //
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(x^{3} \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)^{3} + 3 x \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right) \left(\frac{x^{2} \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} - \frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + \frac{4 x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right) + \frac{x^{2} \left(27 e^{3 x} + \frac{2}{x^{3}}\right) - \frac{3 x^{2} \left(3 e^{3 x} + \frac{1}{x}\right) \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} + \frac{2 x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{3}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + 6 x \left(9 e^{3 x} - \frac{1}{x^{2}}\right) - \frac{6 x \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{e^{3 x} + \log{\left(2 x \right)}} + 18 e^{3 x} + \frac{6}{x}}{e^{3 x} + \log{\left(2 x \right)}}\right)$$