Math 22 Implicit Differentiation

Implicit Differentiation

Consider the equation $x^{2}y=5$. To find ${\frac {dy}{dx}}$, we can rewrite the equation as $y={\frac {5}{x^{2}}}$, then differentiate as usual. ie: $y={\frac {5}{x^{2}}}=5x^{-2}$, so ${\frac {dy}{dx}}=-10x^{-3}$. This is called explicit differentiation. However, sometimes, it is difficult to express $y$ as a function of $x$ explicitly. For example: $y^{2}-2x+4xy=5$

Therefore, we can use the procedure called implicit differentiation

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