Question

find y' of sin((x^2)+(y^2))=4xy. I have already used the chain rule and product rule to get cos((x^2)+(y^2))(2x+2y*y')=4xy'+4y, I just need help isolating y'

Answer 1

\[\cos(x ^{2}+y ^{2})(2x+2yy')=4xy'+4y\]

Answer 2

sin( (x^2)+(y^2) ) = 4xy

((x^2)+(y^2))' cos( (x^2)+(y^2) ) = 4y + 4xy'

2(x+yy') cos( (x^2)+(y^2) ) = 4y + 4xy'

(x+yy') cos( (x^2)+(y^2) ) = 2y + 2xy'
=A


(x+yy')A = 2y + 2xy'

distribute, and collect your like terms ...

Answer 3

You would distribute the A? the A is just a placeholder for cos( (x^2)+(y^2) ) right?