Question

For y=f(x), we define the ______________ of f at x, denoted f′(x), by f′(x)=limh→0(x+ℎ)−(x)/ℎ if the limit exists. If f′(x) exists for each x in the open interval (a,b), then f is said to be _____________ over (a,b).

Answer 1

Answers:

1. derivative
2. differentiable

Explanation:

The derivative is denoted as f ' (x). Sometimes it is written as dy/dx. It depends on context as to which notation is better. Also it's up to personal preference sometimes.

If the derivative f ' (x) exists over some open interval a < x < b, then we say f(x) is differentiable over that interval.