Question
Implicit diff.
y^2 + 4xy +4y^2=40
2yy'+ _______ + 8y*y=0
I am confused with the 4xy.
Would you write this out to be
4x*y'+4y OR
4x*4y' + 4y*4x'?
Please help
y^2 + 4xy +4y^2=40
2yy'+ _______ + 8y*y=0
I am confused with the 4xy.
Would you write this out to be
4x*y'+4y OR
4x*4y' + 4y*4x'?
Please help
Answers
Steve
First off, I suspect a typo. Why have two y^2 terms? I figure you meant
x^2 + 4xy +4y^2=40
Just do things term by term, and don't forget the product rule:
2x + 4y + 4xy' + 8yy' = 0
y'(4x+8y) = -(2x+4y)
y' = -1/2
Weird, huh? Not if you note that
x^2 + 4xy +4y^2 is just (x+2y)^2
x^2 + 4xy +4y^2=40
Just do things term by term, and don't forget the product rule:
2x + 4y + 4xy' + 8yy' = 0
y'(4x+8y) = -(2x+4y)
y' = -1/2
Weird, huh? Not if you note that
x^2 + 4xy +4y^2 is just (x+2y)^2