Suppose That $f$ And $g$ Are Functions That Are Differentiable At $x = 1$

question 57

Essay

Suppose that $f$ and $g$ are functions that are differentiable at $x = 1$ and that $f ( 1 ) = 1 , f ^ { \prime } ( 1 ) = - 3 , g$ $( 1 ) = 2$ , and $g ^ { \prime } ( 1 ) = 5$ . Find $h ^ { \prime } ( 1 )$ .
$$h ( x ) = \frac { x f ( x ) } { x + g ( x ) }$$

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Definitions:

Participant Observation

A qualitative research method in which the researcher immerses themselves in a community or group to observe and participate in its activities.

Semi-Covert

Partially hidden or not openly acknowledged activities or operations, maintaining some level of secrecy or confidentiality.

Covert

Activities or operations carried out secretly or without open acknowledgment.

Qualitative

A research approach focusing on understanding phenomena through observation and interpretation, often dealing with complexities of human behavior and social contexts.