Implicit differentiation and tangent lines

One of these I know is wrong ,one of these I don't understand how to do.

1) Use logarithmic differentiation to find the derivative of the function.http://www.webassign.net/cgi-bin/sym...28ln%28x%29%29

ln(y) = ln(x)ln(sin(x))

F(x) = ln(x)ln(sin(x))

f(x) = ln(x); f'(x) = 1/x

g(x) = ln(sin(x))

g'(x) = cosx/sinx

y'/y = [ln(sin(x))/x] + [ln(x)cos(x)/sin(x)]

y' = y{[ln(sin(x))/x] + [ln(x)cos(x)/sin(x)]}

y' = [sin(x)^ln(x)ln(sin(x))/x] + (ln(x)^2) * cos(x)

Not sure where i went wrong on that one.

2) The curve with equation *y*2 = *x*3 + 3*x*2 is called the Tschirnhausen cubic. -Find an equation of the tangent line to this curve at the point (1, -2).

-Find the points on the curve where the tangent line has a vertical asymptote

I was under the impression I had to derive the function, and then find points where it is undefined, but the question is asking for y, not y'.