Question

Find the differential: y^2 - xe^4 =2

Please show me steps so I can learn, thanks.

Answer 1

http://www.cliffsnotes.com/study_guide/Introduction-to-Differential-Equations.topicArticleId-19736,articleId-19708.html

finally someone who wants to learn: I don't know how to do this exactly, but this website should help you

Answer 2

Try to make it a little easier looking. ie, get it into the form: y= something.

Answer 3

You'll need implicit differentiation for this.
\[y^2-xe^4=2\]Step 1: Take the derivative with respect to x of everything:
\[\frac{d}{dx}y^2-\frac{d}{dx}xe^4=\frac{d}{dx}2\]

***********************************************
As an aside, let's find the derivative of y^2 with respect to x.
Let \(g=y^2\)
\[\frac{d}{dx}y^2=\frac{d}{dx}g\]
\[\frac{dg}{dx}=\frac{dg}{dy} \times \frac{dy}{dx} \text{ by the chain rule}\]\[=2y \times \frac{dy}{dx}\]***********************************************

Going back to the original equation:
\[\frac{d}{dx}y^2-\frac{d}{dx}xe^4=\frac{d}{dx}2\]\[<=> 2y\frac{dy}{dx} - e^4 = 0\]\[<=> \frac{dy}{dx}=\frac{e^4}{2y}\]

Answer 4

Wow that's great, thanks a lot for the help everyone, I really appreciate it.