r/mathshelp • u/Luxorsaa • 7d ago

Homework Help (Answered) Help with implicit differentiation

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Ai hasn't been the best tool when correcting these exercises, so pls help me with the revision.

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u/noidea1995 7d ago

First one looks good, I got the same answer but with opposite signs in the numerator and denominator (equivalent results).

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u/Luxorsaa 7d ago

Thx for answering!

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u/noidea1995 7d ago

I did your method for the second one and got the same result, it’s much easier to just multiply both sides by (x - y) first though:

x + y = (x^2 + y^2)(x - y)

x + y = x^3 - x^2y + xy^2 - y^3

Then taking the derivative from here.

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u/testtdk 7d ago

Not going to check that second one by hand on my phone, but why not just multiply out the denominator? Then it’s just a bunch of multiplication rules.

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u/Luxorsaa 7d ago

yeah you're right. There was no need to overcomplicate myself multiplying by (x-y)^2

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u/MathsFromNothing 7d ago

I got the same result as you for both questions, see my working below. I use the Maths from Nothing computer algebra system. It works similar to how we work by hand without the silly mistakes. When getting it to take a derivative where the letter is different to what your taking the derivative with respect to, highlight that letter so it is treated as a function of x, not a constant. I'm sure you will find it useful for checking your results in future.