Question

Find `"dy"/"dx"` if e^x+y = cos(x – y)

Answer 1

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

∴ `e^(x + y)(1 + "dy"/"dx") = -sin(x - y)."dy"/"dx"(x - y)`

∴ `e^(x + y) + e^(x + y)."dy"/"dx" = -sin(x - y)(1 - "dy"/"dx")`

∴ `[e^(x + y) - sin(x - y)]"dy"/"dx" = -sin(x - y) - e^(x + y)`

∴ `"dy"/"dx" = -[(sin(x - y) + e^(x + y))/(e^(x + y) - sin(x - y))] = (sin(x - y) + e^(x + y))/(sin(x - y) - e^(x + y)`.