Question

Find `"dy"/"dx"` if x = 5t², y = 10t.  

Answer 1

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"`