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Question
Find `"dy"/"dx"` if x = 5t2, y = 10t.
Solution
x = 5t2
Differentiating both sides w.r.t. t, we get
`"dx"/"dt" = 5("2t") = 10"t"`
y = 10t
Differentiating both sides w.r.t. t, we get
`"dy"/"dt" = 10(1) = 10`
∴ `"dy"/"dx" = ("dy"/"dt")/("dx"/"dt")`
∴ `"dy"/"dx" = 10/(10"t")`
∴ `"dy"/"dx" = 1/"t"`
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