I'm supposed to implicitly differentiate sin &#x2061;<!-- ⁡ --> ( x + y ) = 2 x

spockmonkey40

spockmonkey40

Answered question

2022-07-07

I'm supposed to implicitly differentiate sin ( x + y ) = 2 x 2 y. I've already taken the first derivative and got
( d y d x + 1 ) cos ( y + x ) = 2 ( d y d x 1 )

Answer & Explanation

Allison Pena

Allison Pena

Beginner2022-07-08Added 14 answers

( d y d x + 1 ) cos ( y + x ) = 2 ( d y d x 1 )
d y d x cos ( y + x ) + cos ( y + x ) = 2 d y d x + 2
d y d x cos ( y + x ) + 2 d y d x = 2 cos ( y + x )
d y d x ( cos ( y + x ) + 2 ) = ( 2 + cos ( y + x ) )
d y d x = cos ( y + x ) 2 cos ( y + x ) + 2
antennense

antennense

Beginner2022-07-09Added 7 answers

So,
sin ( x + y ) = 2 ( x y )
thus
cos ( x + y ) + d y d x cos ( x + y ) = 2 2 d y d x
Or
cos ( x + y ) ( 1 + d y d x ) = 2 ( 1 d y d x )
Re-arranging
cos ( x + y ) d y d x + 2 d y d x = 2 cos ( x + y )
Hence,
d y d x ( 2 + cos ( x + y ) = ( cos ( x + y ) 2 )
From which
d y d x = cos ( x + y ) 2 cos ( x + y ) + 2

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