Question

Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`

Options

• `e^x`

• `sin^2x`

• `(e^x (sin x - cos x))/(sin^2x)`

• None of these

Answer 1

`(e^x (sin x - cos x))/(sin^2x)`

Explanation:

`y = e^x/sin x`

For `y = u/v, (dy)/(dx) = u^' v - (uv^')/v^2`

∴ `(dy)/(dx) = e^x sin x - (e^x cos x)/(sin x)^2 = (e^x (sin x - cos x))/(sin^2x)`