Question

implicit differentiation 9x^2+y^2=9

Answer 1

what do you think?

Answer 2

assuming you have to find \(\displaystyle\frac{\partial y}{\partial x}\)
\[
9x^2+y^2=9\\
\frac{\partial}{\partial x}(9x^2+y^2)=\frac{\partial}{\partial x}(9)\\
\implies\frac{\partial}{\partial x}(9x^2)+\frac{\partial}{\partial x}(y^2)=0\\
\implies9\frac{\partial}{\partial x}(x^2)+2y\frac{\partial y}{\partial x}=0\\
\implies9(2x)+2y\frac{\partial y}{\partial x}=0\\
\implies 2y\frac{\partial y}{\partial x}=-18x
\]simplify further