f(x) = x+x+x... (x times)

g(x) = x^2

Obviously f(x) = g(x), for example

if x=4 then f(x)=x+x+x+x = 4+4+4+4 = 16

if x=5 then f(x)=x+x+x+x+x = 5+5+5+5+5 = 25

Now let's differentiate both.

f'(x)=d/dx x + d/dx x + d/dx x... (x times)

and since d/dx x = 1, f'(x)=1+1+1... (x times) = x.

g'(x)=d/dx x^2 = 2x

Explain why f'(x) != g'(x).