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# Chain Rule: Tangent of an Exponential

APCALC-S8EOKN

What is the derivative of $y=\tan { ( 5^{ 2x+5 } ) } ,$ with respect to ‘$x$’?

A

$\cfrac{dy}{dx}=4( { 5 }^{ 2x+5 } ) \ln { ( 5 ) } \sin { ( { 5 }^{ 2x+5 } ) }$

B

$\cfrac{dy}{dx}=-( { 5 }^{ 2x+5 } ) \ln { ( 5 ) } \csc ^{ 2 }{ ( { 5 }^{ 2x+5 } ) }$

C

$\cfrac{dy}{dx}=-2( { 5 }^{ 2x+5 } ) \ln { ( 5 ) } \tan { ( { 5 }^{ 2x+5 } ) }$

D

$\cfrac{dy}{dx}=4( { 5 }^{ 2x+5 } ) \ln { ( 5 ) } \cot ^{ 2 }{ ( { 5 }^{ 2x+5 } ) }$

E

$\cfrac{dy}{dx}=2( { 5 }^{ 2x+5 } ) \ln { ( 5 ) } \sec ^{ 2 }{ ( { 5 }^{ 2x+5 } ) }$