post your mental illness itt

[Plug Drugs]

Here.. pretty basic calculus problem. If you want to find the slope of the tangent line at a point on the curve y=x^2, we can pretend the tangent line touches two points on the curve an infinitesimal distance apart.

Slope = Rise / Run
the 'run' is infinitesimal, which we will represent with the variable 'h'

Rise = (x+h)^2 - x^2


x^2 + h^2 + 2xh + -x^2
h


simplify this to 2x+h or just 2x, which is the derivative of y=x^2, giving us the slope of the tangent line at any given point on the curve y=x^2