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

question 102

Multiple Choice

Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ using implicit differentiation. $\frac { e ^ { x } } { y ^ { 2 } } = 16 + e ^ { y }$

• A) \(\frac { y e ^ { x } } { 16 e ^ { x } + 3 y ^ { 2 } e ^ { y } }\)
• B) \(\frac { 2 y e ^ { x } } { e ^ { x } + y e ^ { y } }\)
• C) \(\frac { 2 e ^ { x } + y ^ { 3 } e ^ { y } } { y e ^ { x } }\)
• D) \(\frac { y e ^ { x } } { 2 e ^ { x } + y ^ { 3 } e ^ { y } }\)
• E) \(\frac { y } { 2 + y ^ { 3 } }\)

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Definitions:

Equilibrium Price

The price at which the quantity of a good or service demanded by consumers equals the quantity supplied by producers.

Equilibrium Quantity

The quantity of goods or services supplied is equal to the quantity demanded at the market price.

Supply Decreases

A reduction in the quantity of a good or service that producers are willing and able to sell at a given price.

Late Frost

An unexpectedly cold period occurring late in the spring that can damage or kill crops and plants.