While differentiating an implicit function , I ended up treating du/dx as a fraction and I am not quite happy about that . I want to know whether it's mathematically accurate to do that . Question: Differentiate x(y)^3 with respect to x by not using product rule .
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Do you have any example? – RajSharma Oct 21 '15 at 08:53
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Please be a bit more specific. – SchrodingersCat Oct 21 '15 at 08:56
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I have put down an example . – Abu Bardewa Oct 21 '15 at 08:58
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Do you mean $(x(y))^3$ or $xy^3$? – Git Gud Oct 21 '15 at 09:54
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@GitGud the second one . – Abu Bardewa Oct 21 '15 at 09:55
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1@AbuBardewa This has nothing to do with implicit differentiation, though. This just a partial derivative. – Git Gud Oct 21 '15 at 09:56
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I did not use the product rule . I differentiated it and came to an expression where I ended up treating that as fraction and cancelling it out . I checked it using the product rule as well and it works. So I was wondering how is it possible to treat it as a fraction. – Abu Bardewa Oct 21 '15 at 09:59