Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$

question 42

Multiple Choice

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. $y = ( \sqrt { x } + 2 ) \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right)$

• A) \(\frac { 1 } { 2 \sqrt { x } } \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right) + \left( \frac { 1 } { 2 \sqrt { x } } - \frac { 4 } { x ^ { 3 } } \right) ( \sqrt { x } + 2 )\)
• B) \(\frac { \sqrt { x } } { 2 } \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right) + \left( \frac { \sqrt { x } } { 2 } - \frac { 4 } { x ^ { 3 } } \right) ( \sqrt { x } + 2 )\)
• C) \(\frac { 1 } { 2 \sqrt { x } } \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right) + \left( \frac { 1 } { 2 \sqrt { x } } - 4 x \right) ( \sqrt { x } + 2 )\)
• D) \(\frac { 1 } { \sqrt { x } } \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right) + \left( \frac { 1 } { \sqrt { x } } - \frac { 4 } { x } \right) ( \sqrt { x } + 2 )\)
• E) \(\frac { 1 } { 2 \sqrt { x } } \left( \sqrt { x } + \frac { 2 } { x ^ { 2 } } \right) + \left( \frac { 1 } { 2 \sqrt { x } } + \frac { 4 } { x ^ { 3 } } \right) ( \sqrt { x } + 2 )\)

---

Definitions:

Unpleasant

Causing discomfort, unhappiness, or revulsion; not enjoyable or pleasant.

Operant Conditioning

A learning process through which the strength of a behavior is modified by reinforcement or punishment.

Response

A reaction to a specific stimulus or situation, which can be physical, emotional, or cognitive.

Unconditioned Stimulus

A stimulus that inherently triggers a physiological or emotional response without prior conditioning or learning.