Question

Find `"dy"/"dx"`, if x = e^3t , y = `"e"^(4"t" + 5)`

Answer 1

x = e^3t 

Differentiating both sides w.r.t. t, we get

`"dx"/"dt" = "e"^"3t" * "d"/"dx" (3"t") = "e"^"3t"* (3) = 3 "e"^"3t"`  

y = `"e"^(4"t" + 5)`

Differentiating both sides w.r.t. t, we get

`"dy"/"dt" = "e"^(4"t" + 5) * "d"/"dx" ("4t" + 5) = "e"^(4"t" + 5) * (4 + 0)`

`= 4 * "e"^(4"t" + 5)`

∴ `"dy"/"dx" = (("dy"/"dt"))/(("dy"/"dt")) = (4 * "e"^(4"t" + 5))/(3 "e"^"3t") = 4/3 "e"^("t + 5")`