Question

Differentiate the following without solving for y in terms of x.

1. x²/9 + y²/4 =1
2. x²/4 + y²=1
3. x²+ y²/9 =1

Answer 1

1. ${\frac {2x} 9}+{\frac {2y} 4}*y'=0\implies {\frac {2x} 9}+{\frac {yy'} 2}=0$
2. ${\frac {2x} 4}+ 2y*y'=0\implies {\frac x 2}+2yy'=0$
3. $2x+{\frac {2y} 9}*y'=0$