can you please prove that dy/dx=1?

Answer 1

What is the function? I assume it is

(dy/dx is equal to 1 only if y=x+C whre C is a constant)

To prove use the definition of the derivative which is dy/dx as a limit of delta_x appraching of (delta_y/delta_x)
we have
y2-y1=x2+C-x1-C then
delta_y=x2-X1

delta_y/delta_x=(x2-x1)/(x2-x1)=1 QED
(the is no need to take a limit, however in must be used. I hav eommited it for lack of better representation)

Best

Answer 2

this is not a theory that we need to prove, the equation which has dy/dx=1 is y=x+a

Answer 3

The derivate of y = x + c is dy/dx=1. (c is any number)
The proof.
y + dy = (x +dx) + c
Since y = x + c you get
x + c + dy = x +dx + c
So dy =dx or dy/dx=1

Answer 4

This is true only when y= x+ constant.