I have [itex] u(r,\theta)=r \cos \theta + r^{-1}\cos \theta [/itex] and then am changing coordinates [itex] u(x,y)=|x|+\frac{|x|}{x^2+y^2} [/itex]. I then have to compute the vector [itex] \vec v = (u_x,u_y) [/itex].(adsbygoogle = window.adsbygoogle || []).push({});

The thing is, is the derivative of [itex] |x| [/itex] is [itex] sign\,\,x [/itex]. I don't think we should be dealing with this function. So I'm not sure how I should be dropping the absolute value to get to: [itex] u(x,y)=x+\frac{x}{x^2+y^2} [/itex].

I'm thinking it is from the conversion to polar to cartesian... but I'm not sure. Maybe it is within the definition of [itex] \tan^{-1} [/itex]... but again I'm not sure. Well I'm sick of throwing random darts, so if anyone has any suggestions, I'm all ears :)

Please note that [itex] u(x,y) [/itex] was my conversion from polar coordiantes to cartesian, so this could also be a problem, and might be incorrect.

Thankyou.

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# Homework Help: Another algebra and trig question (maybe not though)

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