Q7 of 147 Page 191

Differentiate w.r.t. x the function
(log x)^{log x}, x > 1

Let y =

Taking logarithm on both sides

⇒ log y = log (log x)^{log x} = log x × log (log x)

Differentiating both sides with respect to x, we get

⇒

∴

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

Differentiate w.r.t. x the function(log x)log x, x > 1