Question

Derivative of e^x sin x w.r.t. e^-x cos x is ______.

Options

• cot x

• - cot x

• e^2x

• - e^2x

Answer 1

Derivative of e^x sin x w.r.t. e^-x cos x is - e^2x.

Explanation:

Let y = e^x sin x and z = e^-x cos x

`therefore "dy"/"dx" = "e"^x (sin x + cos x) and`

`"dz"/"dx" = - "e"^(- x)`(cos x + sin x)

`therefore "dy"/"dx" = ("dy"/"dx")/("dz"/"dx") = - "e"^(2x)`