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Question
Find `"dy"/"dx"`, if x = at2, y = 2at
Solution
x = at2
Differentiating both sides w.r.t. t, we get
`"dx"/"dt" = "d"/"dt" ("at"^2) = "a" "d"/"dt" ("t"^2) = 2 "at"`
y = 2at
Differentiating both sides w.r.t. t, we get
`"dy"/"dt" = "d"/"dt" (2"at") = "a" "d"/"dt" (2"t") = 2 "a"`
∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")) = "2a"/"2at" = 1/"t"`
∴ `"dy"/"dx" = 1/"t"`
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