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Question
Find `("d"y)/("d"x)`, if x = em, y = `"e"^(sqrt("m"))`
Solution: Given, x = em and y = `"e"^(sqrt("m"))`
Now, y = `"e"^(sqrt("m"))`
Diff.w.r.to m,
`("d"y)/"dm" = "e"^(sqrt("m"))("d"square)/"dm"`
∴ `("d"y)/"dm" = "e"^(sqrt("m"))*1/(2sqrt("m"))` .....(i)
Now, x = em
Diff.w.r.to m,
`("d"x)/"dm" = square` .....(ii)
Now, `("d"y)/("d"x) = (("d"y)/("d"m))/square`
∴ `("d"y)/("d"x) = (("e"sqrt("m"))/square)/("e"^"m")`
∴ `("d"y)/("d"x) = ("e"^(sqrt("m")))/(2sqrt("m")*"e"^("m")`
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Solution
Given, x = em and y = `"e"^(sqrt("m"))`
Now, y = `"e"^(sqrt("m"))`
Diff.w.r.to m,
`("d"y)/"dm" = "e"^(sqrt("m"))("d"sqrt("m"))/"dm"`
∴ `("d"y)/"dm" = "e"^(sqrt("m"))*1/(2sqrt("m"))` .....(i)
Now, x = em
Diff.w.r.to m,
`("d"x)/"dm"` = em .....(ii)
Now, `("d"y)/("d"x)` = `(("d"y)/("d"m))/(("d"x)/("dm"))`
∴ `("d"y)/("d"x) = (("e"sqrt("m"))/(2sqrt("m")))/("e"^"m")`
∴ `("d"y)/("d"x) = ("e"^(sqrt("m")))/(2sqrt("m")*"e"^("m")`
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