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Differentiate 103x^6 . sec x ( 3x+2) |
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Answer» Answer: Note that, y = sec x + tan 2 x sec x ,
= sec x ( sec 2 x + tan 2 x ) ,
= sec x { sec 2 x + ( sec 2 x − 1 ) } ,
= sec x ( 2 sec 2 x − 1 ) .
∴ y = 2 sec 3 x − sec x .
∴ d y d x = d d x { 2 sec 3 x − sec x } ,
= 2 d d x { ( sec x ) 3 } − d d x { sec x } ,
= 2 ⋅ 3 ( sec x ) 2 d d x { sec x } − d d x { sec x } ,
= 6 sec 2 x d d x { sec x } − d d x { sec x } ,
= ( 6 sec 2 x − 1 ) d d x { sec x } ,
⇒ d y d x = ( 6 sec 2 x − 1 ) sec x tan x ,
or, what is the same as, { 6 ( tan 2 x + 1 ) − 1 } sec x tan x = ( 6 tan 2 x + 5 ) sec x tan x . Enjoy MATHS.! |
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