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I was looking at the derivation of the derivative of tan(x^2 + 5x + y) on the Wolfram|Alpha. I don't understand the last step, which says the derivative of y is zero. Shouldn't it be y?

Here is the link to the derivation: http://www3.wolframalpha.com/Calculate/MSP/MSP4281a2116fh62dgcef100002h2gfc72529d6a10?MSPStoreType=image/gif&s=11&w=478&h=546

Please note that I couldn't post an image. The link above will display the image from the Wolfram|Alpha website.

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That link returns an error message: Sorry, this page does not exist on the Wolfram|Alpha site. –  Alex Jun 16 '12 at 20:01
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migrated from mathematica.stackexchange.com Jun 16 '12 at 18:43

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1 Answer

up vote 2 down vote accepted

As you can see the derivative of tan(x^2 + 5x + y) is (5+2 x) sec^2(5 x+x^2+y) as you can see that you have not explicitly stated that y is a function of w. So wofram alpha assumes y to be constant, and the derivative of constant is zero. enter image description here

This is what we get for just y

If you specify y as function of x (by y(x)), you get the following result enter image description here

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