Question

If y = log (cos e^x), then `"dy"/"dx"` is:

Options

• cos e^x−1

• e^−x cos e^x

• e^x sin e^x

• −e^x tan e^x

Answer 1

−e^x tan e^x

Explanation:

y = log (cos e^x)

Differentiating w.r.t. x:

`"dy"/"dx" = 1/(cos ("e"^"x")).(-sin "e"^"x")."e"^"x"` .....(chain rule)

`"dy"/"dx"` = −e^x tan e^x