Erm, well to start with x2 = x*xiitjee10 said:We know x^2 = x*x*x*x... x times
If we differentiate both sides with respect to x, we have
2x=1+1+1+... x times
i.e. 2x=x
i.e 1=2
How is it possible or am i making a mistake?
Please helpp!
lurflurf said:Your way of handling addition and multiplication is confused as you have not prperly defined what x times means. That aside the problem with your differentiation is that for a derivative to be correct all x in the function must be allowed to vary, you hold your x times fixed.
x^2=x+x+x+... xtimes
differentiate
2x=x'+x'+x'+... xtimes
+x+x+x+... x' times
=1+1+1+... x times
+x+x+x+... 1 times
=x+x=2x
So the problems were holding the x in "x times" fixed and not properly defining what "x times means.
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