xsin(4x+5y)=ycos(x) I am trying to use implicit differentiation to find dx/dy for this problem but the answer i keep getting is 4xcos(4x+5y)=−ysin(x) and I am stuck.

Matilda Fox

Matilda Fox

Answered question

2022-07-22

x sin ( 4 x + 5 y ) = y cos ( x )
I am trying to use implicit differentiation to find dx/dy for this problem but the answer i keep getting is
4 x cos ( 4 x + 5 y ) = y sin ( x )
and I am stuck.

Answer & Explanation

eyiliweyouc

eyiliweyouc

Beginner2022-07-23Added 15 answers

You're forgetting that x is dependent on y so you have to take chain rule into account. I'll do part of it. Hopefully you can see what to do from there.
d d y ( x sin ( 4 x + 5 y ) ) = product rule ( d d y x ) sin ( 4 x + 5 y ) + x d d y sin ( 4 x + 5 y ) = chain rule d x d y sin ( 4 x + 5 y ) + x cos ( 4 x + 5 y ) d d y ( 4 x + 5 y ) = d x d y sin ( 4 x + 5 y ) + x cos ( 4 x + 5 y ) ( 4 d x d y + 5 )
Does this make sense?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?