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Question
Find `"dy"/"dx"`, if x = e3t, y = `"e"^((4"t" + 5))`
Solution
x = e3t
Differentiating both sides w.r.t. t, we get
`"dx"/"dt" = "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)) xx 4`
`= 4 * "e"^((4"t" + 5))`
∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt"))`
= `(4 * "e"^(4"t" + 5))/(3* "e"^(3"t"))`
`= 4/3 e^(4"t" + 5 - 3"t")`
`= 4/3 "e"^("t" + 5)`
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