In math what does f'(x) mean? That is f prime of x.?

Question

I have no idea what it means and what's the little mark after the f indicate? What is the purpose of f prime of x?

Answer 1

The first derivative of the function f(x) is indicated by f'(x).

Answer 2

This is "f prime x", and it means that you have to differentiate. Example: if f(x) = 13 x ³ + 15 x ² + 1, then f '(x) = 39 x ² + 30 x.

Answer 3

This means the first derivative of f(x) with respect to x. This is a short hand way of writing:

d(f(x))/dx

Answer 4

Some books use for one thing, other books use it for another.

Mostly, it means the derivative of f(x).

This notation doesn't work if f() is a function of two or more variables, that is f(x, y, z, ...)

Answer 5

It's the derivative of f(x), defined as

lim [f(a) - f(x)] / (a-x).
a→x

aka the slope of the line that is tangent to the curve at point (x, f(x))

Answer 6

f'(x) is the differentiation of f(x).
For example:
If f(x)= x^2
f'(x)=2x

Differentiation is used to find rates such gradients of graphs.