Implicit and Explicit Differentiation


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Given that:



Find y' using implicit differentiation. Also find y' writing y as an explicit function of x.




Let's first write y as an explicit function of x:



Now, using the product rule, we get:



Let's try now to use implicit differentiation on our original equality to see if it works out:



We must use the product rule again in the left side:



Now we must substitute y as a function of x to compare it to our first result:



And we got the same result, as expected.

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