Question

obtain dy/dx
4xy+cos(x/y)=y

Answer 1

first for the term 4xy
\[4(y+x \frac{ dy }{ dx })\]

Answer 2

for the second term cos(x/y)
\[-\sin \frac{ x }{ y }*\frac{ y-x \frac{ dy }{ dx } }{ y ^{2} }\]

Answer 3

\[4y+4x \frac{ dy }{ dx }-\frac{ 1 }{ y }*\sin \frac{ x }{ y }+\frac{ x }{ y ^{2} }*\sin \frac{ x }{ y }*\frac{ dy }{ dx }=\frac{ dy }{ dx }\]

Answer 4

collect the coefficients od dy/dx

Answer 5

\[(4x+\frac{ x }{ y ^{2} }*\sin \frac{ x }{ y }-1)=-4y+\frac{ 1 }{ y }*\sin \frac{ x }{ y }\]

Answer 6

sorry ,the left hand side is multiplied by dy/dx

Answer 7

Oh okay lol