- #1
Swetasuria
- 48
- 0
Please explain how this equation is derived.
f'(x)= lim [f(x+h)-f(x)]/h
h→0
Thanks.
f'(x)= lim [f(x+h)-f(x)]/h
h→0
Thanks.
micromass said:Maybe your question should be, "why did who choose this particular definition", or "what is the intuition behind this definition". The answers to these questions are bound to be imprecise though. Is that what you want to ask?
Swetasuria said:Please explain how this equation is derived.
f'(x)= lim [f(x+h)-f(x)]/h
h→0
Thanks.
SteveL27 said:Now if you hold x fixed and let h go to zero, you get the limit of the slope as the two points move closer together.
Swetasuria said:But what do you mean by the limit of the slope?
SteveL27 said:For each position of the moving second point, you can calculate the slope of the line through the two points. If the moving slope gets arbitrarily close to some value, we call that value the limit. Didn't you study limits in class before getting to derivatives?
SteveL27 said:Didn't you study limits in class before getting to derivatives?
Swetasuria said:Yeah, we do but I never really got it.
So, does derivative of a function mean the limit of its slope?
A first principle equation in derivatives is a mathematical formula used to find the derivative of a function at a specific point. It is based on the idea of taking smaller and smaller intervals of the function and finding the slope of the tangent line at that point.
The proof for a first principle equation in derivatives involves using the definition of a derivative and taking the limit as the interval approaches zero. This process shows that the derivative is the slope of the tangent line at a specific point.
The first principle equation in derivatives is important because it is the foundation for finding derivatives of more complex functions. It also helps to understand the relationship between the rate of change of a function and the slope of its tangent line.
The first principle equation in derivatives can be time-consuming and tedious to use for more complex functions. It also assumes that the function is continuous and differentiable at the point in question, which may not always be the case.
The first principle equation in derivatives can be applied in various fields such as physics, economics, and engineering to determine rates of change and optimize systems. It can also be used in financial analysis to calculate the instantaneous rate of return on investments.