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If y = log (cos ex) then find "dy"/"dx". - Mathematics

Sum

If y = log (cos ex) then find `"dy"/"dx".`

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Solution

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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