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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"`
Solution
`"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"`
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