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प्रश्न
If y = log (cos ex) then find `"dy"/"dx".`
उत्तर
Let y = log(cos ex)
By using the chain rule, we obtain
`"dy"/"dx" = "d"/"dx"["log"(cos"e"^"x")]`
`= 1/cos"e"^"x" . "d"/"dx"(cos"e"^"x")`
` = 1/(cos"e"^"x") . (-sin"e"^"x") . "d"/"dx" ("e"^"x")`
` = (-sin"e"^"x")/(cos"e"^"x") . "e"^"x"`
`= -"e"^"x" tan"e"^"x", "e"^"x" ≠ (2"n"+1)pi/2, "n"∈ "N"`
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