$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$

question 210

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $4 \sqrt { \mathrm { y } } - \mathrm { y } = 2 \mathrm { x }$

• A) \(\frac { d y } { d x } = \frac { 2 \sqrt { y } } { 2 - \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 4 } { ( 2 - \sqrt { y } ) ^ { 3 } }\)
• B) \(\frac { d y } { d x } = \frac { 2 } { \sqrt { y } } - 2 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { 2 } { y ^ { 2 } }\)
• C) \(\frac { d y } { d x } = \frac { 2 - \sqrt { y } } { 2 \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 - \sqrt { y } } { 4 y }\)
• D) \(\frac { d y } { d x } = \frac { 2 \sqrt { y } } { 2 - \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 - 2 \sqrt { y } } { \sqrt { y } ( 2 - \sqrt { y } ) ^ { 2 } }\)

Identify the components and functions of the autonomic nervous system and the sympathetic nervous system.

Distinguish between the forebrain, midbrain, and hindbrain, and understand their key functions.

Comprehend the role of the cerebral cortex and its importance to human brain function.

Understand the functions of subcortical structures such as the amygdala, thalamus, and hypothalamus.

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