Let h(x)= 4-x^2 + (x+2)

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let h(x)=4−x2+ln⁡(x+2).h(x)=\sqrt{4-x^2}+\ln(x+2). (The natural logarithm is defined only for positive arguments.) (a) Determine the domain of hh. (b) Find h′(x)h'(x) for all xx in the domain of hh. (c) Determine the domain of h′h'. Provide a clear justification that references the domains of the component functions and any additional restrictions introduced by differentiation.

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