Question

Find y' by implicit differentiation: 1/x + 1/y = 1

Answer 1

\[\frac{1}{x}+\frac{1}{y}=1\]
\[x^{-1}+y^{-1}=1\]
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Differentiate,
\[-x^{-2}-y^{-2}(y')=0\]
\[-y^{-2}(y')=x^{-2}\]
\[(y')=\frac{x^{-2}}{-y^{-2}}\]
\[y'=-\frac{y^2}{x^2}\]

Answer 2

Okay so now: Solve the equation explicitly for y and differentiate to get y' in terms of x.