Mathematics

Problem

Let

f(x)=e^{x}\,\ln^{2} x

for

x>0

. a. (i) Derive an expression for

\dfrac{df}{dx}

. b. (ii) Hence obtain a fully simplified expression for

\dfrac{d^{2}f}{dx^{2}}

. c. (iii) For

x>0

, determine all values of

x

(if any) for which

\dfrac{d^{2}f}{dx^{2}}=0