Question

Find `"dy"/"dx"` if x = at², y = 2at.

Answer 1

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"`