Differentiate w.r.t. x the function

Let y =

Taking logarithm both sides, we get

log y = log [(sin x – cos x)^{(sin x – cos x)}]

⇒ log y = (sin x – cos x) × log (sin x – cos x)

Differentiating both sides with respect to x, we get

⇒

⇒

⇒

∴