Question

If y = log (cos e^x) then find `"dy"/"dx".`

Answer 1

Let y = log(cos e^x)

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"`