Question

Choose the correct alternative.

If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`  then `"dy"/"dx"` = ? 

Options

• `"-y"/"x"`

• `"y"/"x"`

• `"-x"/"y"`

• `"x"/"y"`

Answer 1

`"x"/"y"`

Explanation:

x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`

∴ `"dx"/"dt" = 1/2 ("e"^"t" - "e"^-"t")` and `"dy"/"dx" = 1/2 ("e"^"t" + "e"^-"t")`

∴ `"dx"/"dt" = "y" and `"dy"/"dt" = "x"` 

∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")) = "x"/"y"`