Differentiable Functions

from University of Tokyo 1S1 Mathematical Science Foundation: Differential and Integral Calculus Differentiable Functions

• Definition of a function being differentiable at $x=x_0$
  • “For any small $x-x_0<\delta$, the limit ${\lim }_{x\to x_0}\frac{f(x)-f(x_0)}{x-x_0}$ holds true.”