Y = (x-1) Λ3 derivative

Y = (x-1) Λ3 derivative

y=(x-1)^3
y'=3*(x-1)^2*(x-1)'
=3(x-1)^2.

y=x ² Sin2x, find the 50th derivative of Y

For the n-order derivative of the function product y = f (x) * g (x), there is an expansion formula: Y (n) = C (n, 0) f (x) g (x) (n) + C (n, 1) f (x) (1) g (x) (n-1) + C (n, 2) f (x) (2) g (x) (n-2) +. C (n, n) f (x) (n) g (x). Where y (n) represents the n-order derivative of Y, C (n, 0) is an arrangement and combination, f (x) (n) represents the n-order derivative of F (x), G (

What is the relationship between limit and derivative?

Derivative is defined on the basis of limit. Without limit, there will be no derivative! Then the derivative in turn can calculate some special limits, specifically lobida's law, Taylor's theorem and so on!

The relationship between derivative limit and derivative—— High number ～ Please give an example to illustrate that the following sentence is wrong (the simpler the better) - if f '(x0) is equal to a, Lim [x → x0] f' (x) = a (supplementary known condition: F (x) is defined in a neighborhood of x = x0 and differentiable in a decentralized neighborhood of x = x0) Another weak question: Why does Lim [x → 0] f '(x) not exist

As long as f '(x) is discontinuous at x = X., take the following piecewise function as an example:
[f(x)=x^2sin(1/x) x!=0 or f(x)=0 x=0]
At this time, according to the definition of derivative, f '(0) = 0 can be obtained
But Lim [x → 0] f '(x) does not exist

What is the relationship between limit and derivative I know derivative is a tool to find the limit, but why can derivative find the limit? The derivative is a slope on the curve. How can we get the limit when we get the slope?

This can only be used in some special cases such as 0 / 0, because it can be expressed by its derivative plus a higher-order infinitesimal

What is the relationship between limit and derivative? In learning advanced mathematics these days, the teacher always mentioned that limit is the basis of derivative. I can't see the relationship between limit and derivative. Is there any relationship between them?

When the independent variable X of function y = f (x) produces an increment at a point x0 Δ X, the increment of the function output value Δ Y and argument increment Δ The ratio of X is Δ If the limit a exists when x tends to 0, a is the derivative at x0. From this definition, we can know that the derivative is derived from the limit
It is written as a relation:
f(x0)'=lim(x→x0）[f(x)-f(x0)]/(x-x0).