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Question
Fill in the blank.
If y = `"e"^"ax"`, then `"x" * "dy"/"dx" =`____
Solution
If y = `"e"^"ax"`, then `"x" * "dy"/"dx" =` axy
Explanation:
y = `"e"^"ax"`
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "e"^"ax" * "d"/"dx" ("ax")`
`= "e"^"ax" * ("a")`
`= "a" * "e"^"ax"`
∴ `"dy"/"dx"` = ay
∴ `"x" "dy"/"dx" = "axy"`
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