Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
sin(2*x)
/ 3 ___\ / / 3 ___\ sin(2*x) \
\1 + \/ x / *|2*cos(2*x)*log\1 + \/ x / + ------------------|
| 2/3 / 3 ___\|
\ 3*x *\1 + \/ x //
$$\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(2 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{3 x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)$$
/ 2 \
|/ / 3 ___\ sin(2*x) \ |
||6*cos(2*x)*log\1 + \/ x / + ----------------| |
sin(2*x) || 2/3 / 3 ___\| |
/ 3 ___\ |\ x *\1 + \/ x // / 3 ___\ 2*sin(2*x) sin(2*x) 4*cos(2*x) |
\1 + \/ x / *|----------------------------------------------- - 4*log\1 + \/ x /*sin(2*x) - ------------------ - ------------------- + ------------------|
| 9 5/3 / 3 ___\ 2 2/3 / 3 ___\|
| 9*x *\1 + \/ x / 4/3 / 3 ___\ 3*x *\1 + \/ x /|
\ 9*x *\1 + \/ x / /
$$\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)^{2}}{9} - 4 \log{\left(\sqrt[3]{x} + 1 \right)} \sin{\left(2 x \right)} + \frac{4 \cos{\left(2 x \right)}}{3 x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} - \frac{\sin{\left(2 x \right)}}{9 x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} - \frac{2 \sin{\left(2 x \right)}}{9 x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)}\right)$$
/ 3 / / 3 ___\ sin(2*x) \ / / 3 ___\ sin(2*x) 12*cos(2*x) 2*sin(2*x) \ \
|/ / 3 ___\ sin(2*x) \ |6*cos(2*x)*log\1 + \/ x / + ----------------|*|36*log\1 + \/ x /*sin(2*x) + ----------------- - ---------------- + ----------------| |
||6*cos(2*x)*log\1 + \/ x / + ----------------| | 2/3 / 3 ___\| | 2 2/3 / 3 ___\ 5/3 / 3 ___\| |
sin(2*x) || 2/3 / 3 ___\| \ x *\1 + \/ x // | 4/3 / 3 ___\ x *\1 + \/ x / x *\1 + \/ x /| |
/ 3 ___\ |\ x *\1 + \/ x // / 3 ___\ \ x *\1 + \/ x / / 4*sin(2*x) 4*cos(2*x) 2*cos(2*x) 2*sin(2*x) 2*sin(2*x) 10*sin(2*x) |
\1 + \/ x / *|----------------------------------------------- - 8*cos(2*x)*log\1 + \/ x / - ------------------------------------------------------------------------------------------------------------------------------------- - ---------------- - ------------------ - ------------------- + ------------------- + ------------------ + -------------------|
| 27 9 2/3 / 3 ___\ 5/3 / 3 ___\ 2 2 3 8/3 / 3 ___\|
| x *\1 + \/ x / 3*x *\1 + \/ x / 4/3 / 3 ___\ 7/3 / 3 ___\ 2 / 3 ___\ 27*x *\1 + \/ x /|
\ 3*x *\1 + \/ x / 9*x *\1 + \/ x / 27*x *\1 + \/ x / /
$$\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)^{3}}{27} - \frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right) \left(36 \log{\left(\sqrt[3]{x} + 1 \right)} \sin{\left(2 x \right)} - \frac{12 \cos{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} + \frac{2 \sin{\left(2 x \right)}}{x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)}\right)}{9} - 8 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{2 \sin{\left(2 x \right)}}{27 x^{2} \left(\sqrt[3]{x} + 1\right)^{3}} - \frac{4 \sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} - \frac{2 \cos{\left(2 x \right)}}{3 x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} - \frac{4 \cos{\left(2 x \right)}}{3 x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)} + \frac{2 \sin{\left(2 x \right)}}{9 x^{\frac{7}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} + \frac{10 \sin{\left(2 x \right)}}{27 x^{\frac{8}{3}} \left(\sqrt[3]{x} + 1\right)}\right)$$