Use the process of implicit differentiation to find dx/dy given that sin(x)+sin(3y)=1 Can anyone give me hints or steps on what to do?

ormaybesaladqh

ormaybesaladqh

Answered question

2022-10-24

Use the process of implicit differentiation to find d x d y
given that sin ( x ) + sin ( 3 y ) = 1

Answer & Explanation

vacchetta7k

vacchetta7k

Beginner2022-10-25Added 6 answers

If the implicit derivative confuses you then think of both x and y being functions of t and take d d t of both sides:
cos ( x ) d x d t + 3 cos ( 3 y ) d y d t = 0
Then rewrite as
cos ( x ) d x + 3 cos ( 3 y ) d y = 0
And solve to obtain
d x d y = 3 cos ( 3 y ) cos ( x )

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