hi guys can you please help me with this:

Use logarithmic differentiation to find the derivative of$\displaystyle y=\frac{{x}^{19} (cos(3x)-11)}{2x^3-7}$

I was wondering how to handle the little 3x within cosine, do I chain rule it? If I do I end up with this:

$\displaystyle \frac{dy}{dx}=\frac{{x}^{19}(cos(3x)-11)}{2x^3-7} * (\frac{19}{x} - \frac{sin(3x)}{xcos(3x)-11}-\frac{6x^2}{2x^3-7})$

Is there anything wrong?