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I have $\phi$ which is a function of $x$ and $t$ (=time). And there is a point with coordinates $(x_0,y_0)$ moving with the time. At each time step, the coordinates are changing. I want to find the derivative of $\phi$ with respect to $t$ ($y$ in the equation is a constant):

$$\phi(x,t):=\frac{\Gamma}{2\pi}\left(\arctan\frac{y-y_0(t)}{x-x_0(t)}-\arctan\frac{y+y_0(t)}{x-x_0(t)}\right)$$

Thanks.

Math
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  • Where are you having problems ? Is it applying the chain rule or actually performing the differentiation ? Add the equation into your question & show what you have done. Then we are better placed to help you. – Donald Splutterwit Jul 10 '17 at 20:29
  • Thank you. Please, the equation is already posted in the question. Do I need to take the derivative with respect to Xo and Yo because they are changing with time? – Math Jul 10 '17 at 20:31
  • I dont see $t$ in the picture that contains the definition of your function, it is $t$ instead of $\Gamma$? – Masacroso Jul 10 '17 at 20:38
  • Yeah $ \frac{ \partial \phi}{\partial t} = (\frac{ \partial x_0}{\partial t}\frac{ \partial }{\partial x_0} + \frac{ \partial y_0}{\partial t}\frac{ \partial }{\partial y_0}) [...]$ you need to differentiate the expression ... good luck ! ...lol ... $\ddot \smile$. – Donald Splutterwit Jul 10 '17 at 20:38
  • Thank you. Yo and Xo are function of Time – Math Jul 10 '17 at 20:40
  • @Masacroso I think $(x_0(t),y_0(t))$ are dependent on $t$ ... but their specific dependency are not explicitly given. – Donald Splutterwit Jul 10 '17 at 20:42
  • @Math maybe you mean $x$ and $y$, not $x_0$ and $y_0$. In general the subindex are used to state constants... – Masacroso Jul 10 '17 at 20:42
  • @Masacroso. Thank you.(xo(t),yo(t)) are dependent on t – Math Jul 10 '17 at 20:43
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    Donald Splutterwit. thank you. You mean take the derivative of ϕ with respect to Xo then take it again with respect to Yo then add together? – Math Jul 10 '17 at 20:45
  • which contest math was this from? – jimjim Jul 10 '17 at 21:49

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