May 7th, 2014, 06:55 AM  #1 
Newbie Joined: May 2014 From: India Posts: 12 Thanks: 0  Differentiation 2
If y=(image) then dy/dx=? 
May 7th, 2014, 08:14 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
Surely $y(x)$ is a step function, so therefore has $$\frac{dy}{dx}=\begin{cases}0 & x \notin \mathbb{Z} \\ \text{undefined} & x \in \mathbb{Z} \\ \end{cases}$$ If it's not a step function, then it would seem more sensible to write it as $$y(x) = \int_1^x \frac{1}{\arctan{\left(1+r+r^2\right)}}dr $$ In which case, by the second fundamental theorem of calculus, $$\frac{dy}{dx} = \frac{1}{\arctan{\left(1+x+x^2\right)}}$$ Last edited by v8archie; May 7th, 2014 at 08:22 AM. 
May 7th, 2014, 09:08 AM  #3  
Newbie Joined: May 2014 From: India Posts: 12 Thanks: 0  Quote:
its arctan[1/(1+r+r^2)] also answer is 1/(1+(x+1)^2) Last edited by Raptor; May 7th, 2014 at 09:12 AM. Reason: missed a point  
May 7th, 2014, 09:24 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra  
May 7th, 2014, 09:28 AM  #5  
Newbie Joined: May 2014 From: India Posts: 12 Thanks: 0  Quote:
in our country being a good problesolver is better than being practical if u ever find out how to solve it pls let me know Last edited by Raptor; May 7th, 2014 at 09:28 AM. Reason: grammer  
May 7th, 2014, 10:34 AM  #6 
Newbie Joined: May 2014 From: India Posts: 12 Thanks: 0 
I have solved this... if u don't know how to solve the equation, check the attached image... 
May 7th, 2014, 11:33 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
The problem is that, for the sum to make sense, x must be restricted to integer values. But inn that case, the concept of a limit breaks down and there is no derivative. If x is not an restricted to integers, you get either a step function (as I said before) or the telescoping series fails to telescope (over the reals) and the sum is in fact an integral. So you result for the series is right (and very good), but the differential is wrrong and/or meaningless. Subscribing meaning to meaningless things is mysticism, not maths. 

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differentiation, inverse, trigometric 
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