How do you find dy/dx for the function y=sin(2x+4y)

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Answered question

2022-09-16

How do you find dy/dx for the function y = sin ( 2 x + 4 y )

Answer & Explanation

Zariah Fletcher

Zariah Fletcher

Beginner2022-09-17Added 8 answers

You have an Implicit Function in which y is function of x so you have to derive it as well.
You get:
d y d x = [ cos ( 2 x + 4 y ) ] [ 2 + 4 d y d x ]
where you use the Chain Rule on the sin function.
d y d x = 2 cos ( 2 x + 4 y ) + 4 cos ( 2 x + 4 y ) d y d x
Collecting d y d x
d y d x [ 1 - 4 cos ( 2 x + 4 y ) ] = 2 cos ( 2 x + 4 y )
d y d x = 2 cos ( 2 x + 4 y ) 1 - 4 cos ( 2 x + 4 y )

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