Find the Derivative of the Function $y ( x ) = \sec \left( e ^ { 4 x } \right)$

question 57

Multiple Choice

Find the derivative of the function. $y ( x ) = \sec \left( e ^ { 4 x } \right)$

• A) \(y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)\)
• B) \(y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)\)
• C) \(y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)\)
• D) \(y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)\)
• E) \(y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)\)

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Definitions:

Account

A record that keeps track of all financial transactions related to an asset, liability, equity, revenue, or expense.

Increases

The action or process of becoming larger in quantity, size, amount, or degree in a financial or numerical context.

Asset Account

An account that represents a resource owned or controlled by a business, expected to provide future economic benefits.

Debit

An entry recorded on the left side of an account in double-entry bookkeeping that increases asset or expense accounts, or decreases liability, equity, or revenue accounts.