Q9 of 147 Page 191

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

⇒

∴

Differentiate w.r.t. x the function

(log x)^{log x}, x > 1

Differentiate w.r.t. x the function

cos (a cos x + b sin x), for some constant a and b.

Differentiate w.r.t. x the function

x^x + x^a + a^x + a^a, for some fixed a > 0 and x > 0

Differentiate w.r.t. x the function

, for x > 3