This paper proves whether there is a function, which satisfies the following condition: "differentiable everywhere, but the derivative function is discontinuous everywhere" Because we already know that there is a kind of function which is "continuous everywhere but not differentiable everywhere", but we can't find any proof on the Internet about the existence of this kind of function

This paper proves whether there is a function, which satisfies the following condition: "differentiable everywhere, but the derivative function is discontinuous everywhere" Because we already know that there is a kind of function which is "continuous everywhere but not differentiable everywhere", but we can't find any proof on the Internet about the existence of this kind of function

The conclusion is negative. In fact, the continuous point set of the derivative function of the differentiable function on closed interval I must be dense on I. please refer to question 5 on page 55 of Zhou Minqiang's theory of functions of real variables. The general idea is as follows: first, record F_ N (x) = n [f (x + 1 / N) - f (x)], then f_ Because f is differentiable everywhere, for every x ∈ I

How to take the path when proving that the limit of binary function does not exist?

According to the topic, in order to make the follow-up calculation as simple as possible

Let z = f (x ^ (x + y), X / y), where f (U, V) is a differentiable function, and find ᦉ 8706; Z / ᦉ 8706; X, ᦉ 8706; Z / ᦉ 8706; y

If you don't understand, please ask

It is known that (x + 1) n = A0 + A1 (x-1) + A2 (x-1) 2 + A3 (x-1) 3 + +An (x-1) n, (where n ∈ n *) (1) find A0 and Sn = a1 + 2A2 + 3a3 + +(2) compare the size of Sn and N3, and explain the reason

(1) If x = 1, A0 = 2n (1 point) by deriving the two sides of the equation, n (x + 1) n − 1 = a1 + 2A2 (x − 1) + 3a3 (x − 1) 2 + +Nan (x − 1) n − 1, take x = 2, then Sn = a1 + 2A2 + 3a3 + +nan＝n•3n−1．       … （...

7x-15 = 4x solution?

7x-15 = 4x shift
=>7x-15-4x=0
=>3x-15=0
=>3x=15
=>x=5

An empty barrel weighs 2kg, which is just 1kg less than 30% of the oil contained in this oil surge. How many kilos does this barrel weigh?

(2 + 1) △ 30% + 2, = 10 + 2, = 12 (kg). A: this barrel of oil weighs 12 kg

Judge the continuity and differentiability of piecewise function (with graph)

Continuous but undifferentiable
When x approaches 0 from negative direction, f'x = - 1
When x approaches 0 from positive direction, f'x = 2x = 0

What is the value of X after the operation of the expression "x = (2 + 3,6 * 5), x + 5"?

The answer is 30;
Operation priority: parenthesis > assignment operator > comma
The first is the operation in parentheses. The result of 2 + 3 and 6 * 5 is 30. The priority of the assignment operator is higher than that of the comma operator. The assignment operation is left associative, so the answer is 30

In the Three Gorges, the torrential flow of the Three Gorges in summer is as follows:________ ,_______ ,_________ ,_________ ,_________ .”

Sometimes the emperor sent the White Emperor to Jiangling at dusk. During that time, he ran for thousands of miles to resist the wind

X → 0, what is the order of the following infinitesimal compared with X: 1-cosx, x + tan2

1-cosx → (x ^ 2) / 2 is therefore the higher order infinitesimal of X, and X + tan2 → tan2 is not infinitesimal at all