Find the Derivative of the Following Function $y = 8 ^ { 9 x + 1 }$

question 12

Multiple Choice

Find the derivative of the following function. $y = 8 ^ { 9 x + 1 }$

• A) \(y ^ { \prime } = ( 8 \ln 9 ) 8 ^ { 9 x + 1 }\)
• B) \(y ^ { \prime } = ( 9 \ln 8 ) 8 ^ { 9 x + 1 }\)
• C) \( y ^ { \prime } = ( \ln 9 ) ^ { 9 x + 1 }\)
• D) \(y ^ { \prime } = ( \ln 8 ) 8 ^ { 9 x + 1 }\)
• E) \(y ^ { \prime } = ( \ln 72 ) 8 ^ { 9 x + 1 }\)

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Definitions:

Urine Filtrate

A liquid substance that has been passed through a filter, in this context referring to the substance filtered from the blood through the kidneys before becoming urine.

Simple Cuboidal Cells

A type of epithelial cell that is cube-shaped and forms the lining of various glands and ducts, playing a role in secretion and absorption.

Proximal Tubule

The segment of the nephron in the kidney immediately following the Bowman's capsule that reabsorbs water, ions, and nutrients from the filtrate.

Microvilli

Tiny, finger-like extensions of the plasma membrane of cells, especially epithelial cells, which increase surface area for absorption.