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How to do second derivative implicit differentiation using Wolfram Alpha?

Posted 10 years ago

How do I perform second derivative implicit differentiation using Wolfram Alpha? I'm looking for results that will give me the step-by-step solutions as 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.

Thanks for any assistance.

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

enter image description here

P.S. Cross posted to http://mathematica.stackexchange.com/questions/51705/second-derivative-implicit-differentiation-using-wolfram-alpha-input

POSTED BY: Gary White
5 Replies
POSTED BY: Marco Thiel
Posted 10 years ago
POSTED BY: Gary White
Posted 10 years ago

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POSTED BY: Bill Simpson

Hi Gary,

this probably does not really answer your question. I am also not quite sure what your input was and I cannot reproduce what you get, but if you do the calculation in two steps it works. First you take the first derivative

enter image description here

then calculate another derivative of the first result.

enter image description here

As you see you get to see step-by-step solutions. The second solution contains the first and second derivative. You then need to substitute the first result:

y'[x] + x y''[x] == y[x]/x  /. {y'[x] -> -2 - y[x]/x}

The only thing that remains is to solve for y''[x].

Solve[%, y''[x]]

From you screenshot I see that you have Mathematica and not only Wolfram Alpha, so this recipe should work. You have to do a bit of work by hand, but you get to see all the other intermediate steps shown.

I am not sure how to get this with step-by-step solutions with one query to Wolfram Alpha. What was your input?

Cheers, M.

POSTED BY: Marco Thiel
Posted 10 years ago

Whoops. FYI - I replied at the end of the page instead of hitting the reply button on your post.

POSTED BY: Gary White
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