Question

Derivative of `e^(sin^2x)` with respect to cos x is ______.

Options

• `sin x  e^(sin^2x)`

• `cos x  e^(sin^2x)`

• `−2 cos x  e^(sin^2x)`

• `−2 sin^2 x cos x  e^(sin^2x)`

Answer 1

Derivative of `e^(sin^2x)` with respect to cos x is `bbunderline(−2  cos  x (e^(sin^2x)))`.

Explanation:

u = `e^(sin^2x) and v = cos x`

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

and `(dv)/(dx) = -sin x`

Thus, `(du)/(dv) = (du"/"dx)/(dv"/"dx)`

= `(e^(sin^2x).2sin x.cosx)/-sin x`

= `-2 cos x  e^(sin^2x)`