If xy=tan-1(xy)+cot-1(xy), then dydx is equal to
yx
-yx
xy
-xy
Explanation for the correct option.
We know that tan-1x+cot-1x=π2.
So, xy=tan-1(xy)+cot-1(xy) can be written as
xy=π2
By differentiating with respect to x, we get
xdydx+1y=0byproductrule⇒xdydx=-y⇒dydx=-yx
Hence, option B is correct.