Mathematics

Problem

Let

h(x)=\sqrt{4-x^2}+\ln(x+2).

(The natural logarithm is defined only for positive arguments.) (a) Determine the domain of

h

. (b) Find

h'(x)

for all

x

in the domain of

h

. (c) Determine the domain of

h'

. Provide a clear justification that references the domains of the component functions and any additional restrictions introduced by differentiation.