Melody,You are too complicated...
$$lny=ln(e+1)^3+\(\frac{1}{2}(x+1)-ln(x+2)-2ln(sin(3x+2))
\(\frac{y'}{y}=0+\(\frac{1}{2(x+1)}-\(\frac{1}{x+2}-\(\frac{2cos(3x+2)3}{sin(3x+2)}
y'=y[\(\frac{1}{2(x+1)}-\(\frac{1}{x+2}-\(\frac{6cos(3x+2)}{sin(3x+2)}]
y'=\(\frac{(e+1)^3\sqrt{x+1}}{(x+2)sin^2(3x+2)}[\(\frac{1}{2(x+1)}-\(\frac{1}{x+2}-6cot(3x+2)]$$
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