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I'm a complete newbie to Mathematica. I've been using Wolfram Alpha Pro as well as MS Mathematics for a few months but wanted to dive into using a more powerful tool.

I'm having a problem with calculating a simple derivative and I can't figure out what I'm doing wrong. I tried using free-form input after unsuccessfully trying to use Mathematica syntax but I get the same results. The same query works fine in Wolfram Alpha Pro.

I'm getting pages of repetitive output. Here are a couple of screenshots. The second one is a continuation from further down showing "MaxFormatDepthExceeded" errors.

Any help is greatly appreciated. I apologize for such a basic question.

P.S. I've added a 3rd screenshot to illustrate the successful results for the same query in Wolfram Alpha Pro.

As an aside, can anyone suggest any resources to quickly jump-start my usage of Mathematica? I started to go through the documentation but some of it was quite dense and assumed a level of knowledge that I don't yet have as a first semester calculus student who hasn't done math in some time.

screenshot 1 screenshot 2 same query in Wolfram Alpha Pro

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closed as off-topic by Michael E2, rasher, bobthechemist, Öskå, Kuba Jun 26 at 11:45

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1  
Your definition is rather confusing. You use == which is an equality test, and seem to define y in terms of both x and y. How would you define the derivative of an equation? –  Sjoerd C. de Vries Jun 25 at 17:24
    
I'm not sure how to answer your question. I'm attempting to do implicit differentiation of that equation. I've added a screenshot of the successful results for the same query in Wolfram Alpha Pro. I realize that I might be butchering the terminology but as a first semester calculus student I'm still learning so feel free to correct me. BTW, I didn't put the == in there; that was done as Mathematica's interpretation of the free-form query. When I initially attempted to use Mathematica syntax I used a single =. Thanks for your help. –  WXB13 Jun 25 at 17:53

2 Answers 2

up vote 2 down vote accepted

I don't get the same output as you, when running from a fresh kernel:

enter image description here

Of course, this probably isn't too good either, as we've not indicated that $y$ is a function of $x$. Using the WA interface, I suppose I'd do something like so:

enter image description here

Of course, you've still got to solve for $y'$:

Solve[%, y'[x]]
(* Out: 
   {{y'[x] -> -(Tan[y[x]]/(-1 + x*Sec[y[x]]^2))}} 
*)

With a little practice, you'll be able to roll this into one line in Mathematica:

Solve[D[y[x] == x*Tan[y[x]], x], y'[x]]
(* Out: 
   {{y'[x] -> -(Tan[y[x]]/(-1 + x*Sec[y[x]]^2))}} 
*)

As far as your funky output goes, I strongly suspect that, prior to your In[10], you executed a command along the lines of y=xtan[y], which will certainly lead to a recursion problem. Worse, y will now be defined in a way that simply referring to it will again lead to a recursion problem Keep in mind that Mathematica syntax is precise, unlike that of WA.

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Well, that explains it. I restarted the kernel and it worked as expected. I also clicked on the "Show all results" button after running this and it showed the result I was looking for: y'(x) = tan(y)/(1-x sec^2(y)) using this command: >Solve[Dt[y[x] == x*Tan[y[x]], x], Derivative[1][y][x]] I'm not clear on the all of the differences between this Solve syntax and yours. I believe that D is partial and Dt is a total derivative but I haven't researched exactly what that means yet. Now if I can just figure out how to evaluate at a specific point I'll be golden. Thanks. –  WXB13 Jun 25 at 18:54
    
It looks as if my markdown isn't working as expected. I'll try to fix that. –  WXB13 Jun 25 at 18:59
    
Hmmm...I exceeded the edit time limitation for comments. –  WXB13 Jun 25 at 19:01
    
Glad it helped! Markdown in comments is somewhat different than markdown in a post, I believe. –  Mark McClure Jun 25 at 19:06
D[y[x] == x*Tan[y[x]], x]

Derivative[1][y][x] == Tan[y[x]] + x Sec[y[x]]^2 Derivative[1][y][x]

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Bob, I tried that and got similar (i.e. unsuccessful) results. –  WXB13 Jun 25 at 18:13
    
Yes, I restarted the kernel and it fixed the problem. I'm guessing that Clear[y] is a more granular approach that only flushes the contents of the y variable. IIRC, I think that I tried quitting & restarting Mathematica and it didn't fix the problem. Thanks. –  WXB13 Jun 25 at 19:07

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