Implicit and Explicit Differentiation


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.

Return to Implicit Differentiation

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