Mathematics

Problem

Let

y=e^{2x}\,\ln x

for

x>0

. a. (i) Compute

\dfrac{dy}{dx}

. b. (ii) Hence find

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

. c. (iii) Determine the set of all

x>0

for which

\dfrac{d^{2}y}{dx^{2}}>0