Q5 of 354 Page 12

Differentiate the following functions with respect to x :
(log x)^x

Let y = (log x)^x

Taking log both the sides:

⇒ log y = log (log x)^x

⇒ log y = x log (log x) {log x^a = alog x}

Differentiating with respect to x:

Put (log x)^x

Differentiate the following functions with respect to x :

(1 + cos x)^x

Differentiate the following functions with respect to x :

(log x)^{cos x}

Differentiate the following functions with respect to x :

(sin x)^{cos x}

Differentiate the following functions with respect to x :(log x)x