taking log on both sides
logy= logxsinx +log (sinx)x
logy = sinxlogx + xlog sinx
differentiating
1/y * dy/dx = sinx / x + logx cosx + logsinx + x cosx/sinx
dy/dx = y * (sinx/x +cosxlogx +logsinx + xcosx/sinx)
= (xsinx +sinxx) ( sinx/x +cosxlogx +logsinx +xcosx/sinx)