Question

what is the exact definition of a derivative?

Answer 1

\[f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}\]

Answer 2

It is basically the rate of change of a variable with respect to another. When a particular element is changed by infitesimal amount , what is the change in a function over that element.

Answer 3

so... it is just delta?

Answer 4

np its, delta (x) over delta (y). The definition provided by Across is very accurate (fundamental definition). it says change in function value when x is changed by h.

Answer 5

ahhhh

Answer 6

A derivative is a function of the slope of the tangent line of a curve at any point.

Answer 7

so when you add "h" amount the derivative is the change in the function...

Answer 8

A derivative [of a function] is [another] function [which tells us] the slope of the tangent line of [the] curve at any point. :)

Answer 9

thanks, that helped allot

Answer 10

\[\lim_{\Delta x->0}\frac{\Delta y}{\Delta x}=\frac{dy}{dx}\]

Answer 11

Whereas \(\frac{\Delta y}{\Delta x}\) gives us the average rate of change over an interval; \(\frac{dy}{dx}\) gives us the instantaneous rate of change at any given point.

hope that formats right lol