Q3 of 147 Page 178

Differentiate the functions given in w.r.t. x.
(log x)^{cos x}

Given: (log x)^{cos x}

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

Taking log on both sides, we get

log y = log(log x)^{cos x}

⇒log y = cos x.log(log x)

Now, differentiate both sides with respect to x

Differentiate the functions given in w.r.t. x.

cos x . cos 2x . cos 3x

Differentiate the functions given in w.r.t. x.

x^x – 2^{sin x}

Differentiate the functions given in w.r.t. x.

(x + 3)². (x + 4)³. (x + 5)⁴

Differentiate the functions given in w.r.t. x.(log x)cos x