Question

We know d[x^2]/dx is 2x. However, if we write x^2 as x xs, we get:
d[x^2]/dx = d[x+x+ . . .+x (x times)]/dx,
i.e. d[x^2]/dx = dx/dx+dx/dx+ . . . +dx/dx (x times),
i.e. d[x^2]/dx = 1+1+ . . . +1 (x times),
i.e. d[x^2]/dx = x.

Where is the logic wrong here?

Answer 1

product rule d/dx(x.x)=1x+1x=2x

Answer 2

d/dx of x^3=3x^2 or d/dx (x.x.x) = 1.x.x +x.1.x+x.x.1=3x^2

Answer 3

I see, makes sense. Thanks