Find $y ^ { \prime }$ When $4 x \sin y + 5 y \ln x = 11$

question 33

Multiple Choice

Find $y ^ { \prime }$ when $4 x \sin y + 5 y \ln x = 11$

• A) \(\frac { - ( 4 x \sin y + 5 y ) } { x ( 4 x \cos y + 5 \ln x ) }\)
• B) \(\frac { - ( 4 x \sin y + y ) } { x ( 4 x \sin y + 5 \ln x ) }\)
• C) \(\frac { - ( 4 x \cos y + 5 ) } { ( 4 y \cos y + 5 x ) }\)
• D) \(\frac { - ( 5 x \sin y + 4 y ) } { ( 4 x \cos y + 5 \ln x ) }\)

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Definitions:

Pleiotropic Genes

Genes that have an effect on multiple, seemingly unrelated phenotypic traits, reflecting the complexity of gene expression in organisms.

Phenotype

The set of observable characteristics or traits of an organism resulting from the interaction of its genotype with the environment.

Black Hair

A hair color type characterized by the presence of eumelanin, resulting in a darker shade.

Genotype

The genetic makeup of an organism, consisting of both the visibly expressed traits and those not readily observable.