Q8 of 354 Page 12

Differentiate the following functions with respect to x :
e^{x log} ^x

Let y = e^{x log x}

Taking log both the sides:

⇒ log y = log (e)^{x log x}

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

⇒ log y = x log x {log e = 1}

Differentiating with respect to x:

Put e^{x log} ^x :

{ e^{log a} = a; alog x = x^a}

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 :

(sin x)^{log x}

Differentiate the following functions with respect to x :

10^{log sin x}

Differentiate the following functions with respect to x :ex log x