Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ 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 /
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(\frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 x \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)$$
/ 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)/ /
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(x^{2} \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)^{2} + \frac{x^{2} \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} - \frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + \frac{4 x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)$$
/ 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)/ //
$$\left(e^{3 x} + \log{\left(2 x \right)}\right)^{x^{2}} \left(x^{3} \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right)^{3} + 3 x \left(\frac{x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right) \left(\frac{x^{2} \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} - \frac{x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + \frac{4 x \left(3 e^{3 x} + \frac{1}{x}\right)}{e^{3 x} + \log{\left(2 x \right)}} + 2 \log{\left(e^{3 x} + \log{\left(2 x \right)} \right)}\right) + \frac{x^{2} \left(27 e^{3 x} + \frac{2}{x^{3}}\right) - \frac{3 x^{2} \left(3 e^{3 x} + \frac{1}{x}\right) \left(9 e^{3 x} - \frac{1}{x^{2}}\right)}{e^{3 x} + \log{\left(2 x \right)}} + \frac{2 x^{2} \left(3 e^{3 x} + \frac{1}{x}\right)^{3}}{\left(e^{3 x} + \log{\left(2 x \right)}\right)^{2}} + 6 x \left(9 e^{3 x} - \frac{1}{x^{2}}\right) - \frac{6 x \left(3 e^{3 x} + \frac{1}{x}\right)^{2}}{e^{3 x} + \log{\left(2 x \right)}} + 18 e^{3 x} + \frac{6}{x}}{e^{3 x} + \log{\left(2 x \right)}}\right)$$