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How would you perform second derivative implicit differentiation using Wolfram Alpha input? The reason that I'm using WA input is that it gives you step-by-step solutions and I'm a first year calculus student trying to figure things out.

I've tried all of the obvious queries that I can think of without getting the desired results. If I type just the equation in it will give the results I'm seeking but without the step-by-step solution since it is not the primary output for the query.

Here's an example of the results I get from just entering the equation x^2 + xy = 5 (w/desired result circled):

equation results

*****P.S. Cross posted to community.wolfram.com/groups/-/m/t/283665?p_p_auth=kD3FBYSv ***

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  • $\begingroup$ fyi, cross posted community.wolfram.com/groups/-/m/t/283665?p_p_auth=kD3FBYSv please mention this in your question on both sites so not to waste people time duplicating answers and efforts. $\endgroup$
    – Nasser
    Commented Jun 27, 2014 at 16:57
  • $\begingroup$ Done. Thanks for mentioning that. $\endgroup$
    – WXB13
    Commented Jun 27, 2014 at 20:33
  • $\begingroup$ If you're using Mathematica, why do this on W|A? $\endgroup$
    – Michael E2
    Commented Feb 24, 2018 at 1:12
  • $\begingroup$ @MichaelE2, the answer to your question is in my original post. $\endgroup$
    – WXB13
    Commented Mar 18, 2018 at 23:46
  • $\begingroup$ OK, that's what I thought, but "Some kinds of questions are considered off-topic: Questions on Wolfram Alpha..." (mathematica.stackexchange.com/help/on-topic). This does not seem to be a question on using Mathematica, either to access W|A or to process its results. $\endgroup$
    – Michael E2
    Commented Mar 19, 2018 at 1:27

1 Answer 1

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D[x^2 + x y[x] == 5, {x, 1}]
sol1 = Solve[%, y'[x]]
D[x^2 + x y[x] == 5, {x, 2}]
sol2 = Solve[%, y''[x]]
sol2 /. sol1 // Simplify

enter image description here

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  • $\begingroup$ Thanks but Wolfram Alpha doesn't recognize that and entering it as Mathematica input doesn't give me the step-by-step solution that I'm seeking. $\endgroup$
    – WXB13
    Commented Jun 27, 2014 at 15:35
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    $\begingroup$ @GaryWhite I think my answer is a step by step solution for this example,if you learn something in your calculus class. $\endgroup$
    – Apple
    Commented Jun 27, 2014 at 15:38
  • $\begingroup$ Yes, I see that and I do appreciate your help. Unfortunately, this is still not what I'm looking for. The Wolfram Alpha step-by-step solutions are more granular and come with text explaining each step. $\endgroup$
    – WXB13
    Commented Jun 27, 2014 at 15:57
  • $\begingroup$ @Gary If you want the most "granular" thing: Stay with Wolfram Alpha (although I think that your question received a nice answer). $\endgroup$
    – eldo
    Commented Jun 27, 2014 at 20:52

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