where is the error?

Question

We know that ,x^2(xpower2)=x+x+x+........x terms
Differentiate with respect to x
We get,
2x=(1+1+1+.........xterms)
that implies
2x=x*1
2=1
But, this is not possible.
Where is the error in this proof

Answer 1

The error is in the assumption that the derivative of "x + x + x + ... x terms" is equal to "1 + 1 + 1 + ... x terms." In actuality, "x + x + x + ... x terms" has a second dependence on x, in the mention of "x terms," which is not accounted for in your proposed derivative. If you instead rewrite x^2 as x*x and take the derivative using the product rule, you'd have x*1 + 1*x = 2x, the correct result. Or, if you prefer to retain the atypical addition expansion, you need to add 1 to each term of 1, to account for the derivative of the x in the number of terms.

Answer 2

when you have 2x=x you divide by x. That is not a technically correct operation.

2x-x=0
x(2-1)=0
x=0 or (1) = 0

This only works when x = 0

Answer 3

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Answer 4

2x - 1*x = 0
x = 0

Answer 5

X terms is not differentiatable

Answer 6

x^2 not equal to x+x+x+......x terms.
Give the value of x as 2.
2^4=16
if wat u said was right then 2+2+2+2 should be 16 but its 8.
Hence x^2 is not wat u thought.
x^2=x*x
Now differentiate with respect to x
2x=x*1+x*1 ( as d/dx(uv)=u*dv/dx +v*du/dx )
so, 2x=2x.
Now its proved.

Answer 7

x is not equal to x*