Find the Derivative of the Function $$f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$$

question 3

Multiple Choice

Find the derivative of the function.
$$f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$$

• A) \(\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) ^ { 2 } }\)
• B) \(\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) }\)
• C) \(\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) ^ { 2 } }\)
• D) \(\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) }\)

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Definitions:

Client's Feelings

The emotional states or responses experienced by a client, which are important aspects to address and understand in counseling or therapy.

Guilty

A legal status or feeling indicating that an individual is responsible for committing a crime or has a sense of culpability in a personal or moral context.

Reflection of Meaning

The process of discussing and exploring the deeper significance or personal importance of topics, experiences, or emotions brought up in a therapeutic or counseling session.

Reflection of Feeling

A therapeutic technique where the therapist echoes the client's emotions back to them, validating their feelings and encouraging deeper exploration of these emotions.