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# Differentiation of functions defined implicitly!? (AQA C4) watch

1. Can someone explain how to do this for me? I missed one lesson and a tonne of confusion then ensued! I've gone through it in my textbook like I do with everything else, but I still can't make real sense of it

Thanks peoples
2. Let's say we have the implicit equation xy^2 = 0, and we want to differentiate with respect to x (to find 'horizontal' stationary points, say). Then because we have an equality, we can differentiate both sides:

Using the product rule on the LHS, we get that

The most important thing about implicit differentiation is that we can regard y as a function of x and use the chain rule on the 2nd term:

We can differentiate the first term (to get 2y) and then we just leave the second term as it is. Then, we get something which looks like and we can solve for dy/dx:

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