Q9 of 354 Page 12

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

Let y = (sin x)^{log x}

Taking log both the sides:

⇒ log y = log (sin x)^{log x}

⇒ log y = log x log sin x {log x^a = alog x}

Differentiating with respect to x:

Put (sin x)^{log x} :

Differentiate the following functions with respect to x :

(sin x)^{cos x}

Differentiate the following functions with respect to x :

e^{x log} ^x

Differentiate the following functions with respect to x :

10^{log sin x}

Differentiate the following functions with respect to x :

(log x)^{log x}

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