Can anyone tell me how to find the derivative of:

xy = tan(xy) and of

x² =arctan(y)/(1 + y²)

Very much appreciated, as soon as possible please, I really have no clue when there is both x and y inside the brackets!!

Use implicit differentiation and the chain rule.

xy=tan(xy)

xy'+y=(xy'+y)sec^{2}(xy)

xy'+y=xy'sec^{2}(xy)+ysec^{2}(xy)

xy'-xy'sec^{2}(xy)=ysec^{2}(xy)-y

xy'(1-sec^{2}(xy))=y(sec^{2}(xy)-1)

xy'(1-sec^{2}(xy))=-y(1-sec^{2}(xy))

y'=\frac{-y}{x}