Ok, here's the problem. Your differentiation of $\displaystyle \frac{dy}{du}=u x^{u-1}$ is only valid if $\displaystyle u$ is a constant. In this case, it's not. I would recommend logarithmic differentiation.
Ohhhh.
Ok so here's what I got this time round:
lny = sinx.lnx
and simplified it to give
dy/dx = y(lnxcox + sinx/x)
when x=pi/2, y=pi/2
and dy/dx= 1
Hence the tangent has gradient of 1 and passes through (pi/2, pi/2)
so its equation is: y=x
is it correct this time?
if so, how can we prove b?
Thank you!