Question

Find `"dy"/"dx"` if cos (xy) = x + y

Answer 1

cos (xy) = x + y
Differentiating both sides w.r.t. x, we get
`-sin(xy)."d"/"dx"(xy) = 1 + "dy"/"dx"`

∴ `-sin(xy)[x"dy"/"dx" + y"d"/"dx"(x)] = 1 + "dy"/"dx"`

∴ `-sin(xy)[x"dy"/"dx" + y xx 1] = 1 + "dy"/"dx"`

∴ `-xsin(xy)"dy"/"dx" - ysin(xy) = 1 + "dy"/"dx"`

∴ `-"dy"/"dx" -sin(xy)"dy"/"dx" = 1 +  ysin(xy)`

∴ `-[1 + x sin(xy)]"dy"/"dx" = 1 +  ysin(xy)`

∴ `"dy"/"dx" = (-[1 + ysin (xy)])/(1 + x sin(xy)`.