WE KNOW

3^2=3+3+3

5^2=5+5....5 TIMES

SO x^2=x+x+x.....xtimes

differentiating both sides

d(x^2)/dx=d(x+x+....x times)/dx

=>2x=1+1+1....xtimes

=>2x=x

so, 2=1

adding 3 on both sides

we get

5=4 !!

BUT WE KNOW

d(x^2)/dx=2x

but here we get x...how ??

whats the mistake here plz tell....

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

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

hence ^, d(x²)/dx = 2*x^{2-1 =}2x

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,

Ashwin (IIT Madras).