# WE KNOW3^2=3+3+35^2=5+5....5 TIMESSO x^2=x+x+x.....xtimesdifferentiating both sidesd(x^2)/dx=d(x+x+....x times)/dx=>2x=1+1+1....xtimes=>2x=xso, 2=1adding 3 on both sideswe get5=4  !!BUT WE KNOWd(x^2)/dx=2xbut here we get x...how ??whats the mistake here plz tell....

abhishek f
14 Points
11 years ago

there is a problem in diff. d expression.

when u write x+x+x+x }x times , u put a constraint on x dat it can take only natural number values.

Therefore its grapgh will be points on integral values(+ integers) and not a continuos function. It will be discrete and hence non differentiable.

x=1 y=1

x=2 y=4

but x=0.4 is not in domain

35 Points
11 years ago

In differential , formula is d(xn)/dx = n * x n-1

hence , d(x2)/dx = 2*x2-1 =2x

290 Points
11 years ago

Hi Shubam,

x^2 = x + x + x +..... xtimes, is valid only when x is an integer.

So this equation is valid only for integral values of x.

So x cannot take non-integral values.

If you plot the graph, it is discontinuous for the entire range of real numbers.

As it is not continuous, you cannot differentiate it (that is where the mistake is).

Regards,