The difference between derivative and differential

The difference between derivative and differential

Upstairs, the problem is the difference between derivative and differential. How do you talk about the difference between differential and integral? For a univariate function y = f (x), derivative and differential are no different. The geometric meaning of derivative is the instantaneous rate of change of curve y = f (x), that is, tangent slope. Differential refers to the ratio of the increment of dependent variable to the increment of independent variable △ y =

If integral is the inverse of derivative, what is the relationship between differential and derivative? (natural language narration)

For function f (x), DF / DX is derivative, DF is differential, and derivative is an operation, so it can be regarded as the inverse operation of indefinite integral, which is the quotient of function differential and independent variable differential. It should be said that differential is not an operation in a strict sense

What's the difference between differential and derivative

(1) Different origins (definitions): the origin of derivative is the rate of change of function value with the increment of independent variable, that is, the limit of △ Y / △ X. differential originates from microanalysis. For example, △ y can be decomposed into the sum of a △ X and O (△ x), and its linear principal part is called differential. When △ x is very small, the value of △ y is mainly determined by differential a △ x, and O (△ x) has little effect on its size
(2) Different geometric meanings: the value of the derivative is the slope of the tangent at the point, the value of the derivative is the increment of the ordinate along the tangent direction, and △ y is the increment of the ordinate along the curve direction. You can refer to the graphics of any textbook for understanding
(3) Connection: derivative is the quotient of differential (derivative) y '= dy / DX, and differential dy = f' (x) DX. The formula itself also reflects their differences
(4) Relation: for univariate functions, differentiable must be differentiable, differentiable must be differentiable

The difference between derivative and differential is explained in English

Derivative, denoted by F '(x) differential, denoted by DF (x) that f (x) has derivative at x is equivalent to f (x) is differential at x, and DF (x) = f' (x) DX

Given that the inequality T / T ^ 2 + 9 ≤ a ≤ T + 2 / T ^ 2 is constant on t ∈ (0, √ 2), the value range of real number a is solved by derivative method A quick solution by adding derivative

1. F (T) = t / (T ^ 2 + 9) find the derivative f '(T) = (9-t ^ 2) / (T ^ 2 + 9) ^ 2 Let f' (T) = 0 get t = ± 3. It can be seen that the function is monotonic on t ∈ (0, √ 2). Substitute 1 into f '(T) > 0. Its maximum value is LIM (T - > √ 2) t / (T ^ 2 + 9) = √ 2 / 11 ≤ A2, f (T) = t + 2 / T ^ 2. Find the derivative f' (T) = - 2 / T ^ 3 is √ 2 at t ∈ (0, √ 2)

Let the derivative of function f (x) on R be f '(x), and 2F (x) + XF' (x) > X2, the following inequality is constant in R () A. f（x）＞0 B. f（x）＜0 C. f（x）＞x D. f（x）＜x

∵2f（x）+xf′（x）＞x2，
Let x = 0, then f (x) > 0, so B and D can be excluded
If f (x) = x2 + 0.1, the known condition 2F (x) + XF '(x) > x2 holds,
However, f (x) > x may not be true, so C is also wrong, so choose a
So choose a