After you reach the point where you have $\displaystyle \ln{y} = \:3x\cdot\ln(\sin 5x)$. Differentiate both sides. To do so, use

the chain rule on the the left hand side: $\displaystyle [\ln{y}]' = \frac{y'}{y}$. That done, use the chain and product rules on the

right hand side; I think you know how (it's the product of two functions one of which is a composite, just

like the problem from the other thread). Having done that, multiply both sides by $\displaystyle y$, then you are done!