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