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The difference between differential and integral?
Differential: let the independent variable of function y = f (x) have a modified variable △ x, then the approximate value f ~ (x) * △ X of the corresponding change △ y of the function is called the differential of function y. ("~" represents the derivative) is recorded as dy = f ~ (x) △ X. it can be seen that the concept of differential is obtained on the basis of the concept of derivative. The differential of independent variable is equal to self variable
What is the difference between integral and differential?
Differential: if the independent variable of function y = f (x) has a modified variable △ x, then the approximate value f ~ (x) * △ X of the corresponding change △ y of the function is called the differential of function y. ("~" represents the derivative) is recorded as dy = f ~ (x) △ X. it can be seen that the concept of differential is obtained on the basis of the concept of derivative. If the differential of independent variable is equal to the change of independent variable, replace △ x with DX, and the differential is written as dy = f ~ (x) DX is transformed into: dy / DX = f ~ (x), so the derivative is also called derivative. Integral: it is an inverse problem of differential science. All the original functions of function f (x) are called f (x) or F (x) DX indefinite integral. It is recorded as ∫ f (x) DX. If f (x) is the original function of F (x), then ∫ f (x) DX = f (x) + C C is any constant, which is called indefinite integral constant. For definite integral, Its concept is different from that of indefinite integral. Definite integral Q comes from the limit. It is obtained by calculating the sum of infinite small quantities in a change process with "invariance" instead of "change" and "straight" instead of "curve", and finally taking the limit. Therefore, indefinite integral and definite integral are not only one constant difference, even if they are only one constant difference in calculation, And the algorithm is basically the same. The relationship between them is established through the "Newton Leibniz formula". The formula is right and wrong ∫ f (x) DX = f (b) - f (a) integral lower limit a and upper limit B
What is the difference between differential and integral?
Integrals are generally divided into indefinite integrals, definite integrals and calculus. 1.0 indefinite integrals Let f (x) be an original function of function f (x). We call all original functions f (x) + C (C is any constant) of function f (x) as indefinite integrals of function f (x). It is recorded as ∫ f (x) DX. Where ∫ is called the integral sign and f (x) is called the integrand
The difference between differential and integral in Mathematics
Integrals are generally divided into indefinite integrals, definite integrals and calculus. 1.0 indefinite integrals Let f (x) be an original function of function f (x). We call all original functions f (x) + C (C is any constant) of function f (x) as indefinite integrals of function f (x). It is recorded as ∫ f (x) DX. Where ∫ is called the integral sign and f (x) is called the integrand
The relationship and difference between differential and integral?
Differential and integral are mutually inverse processes
Differential method of composite function, thank you in detail
y=f(g(x))
dy/dx=df(g(x))/d(g(x)) * d(g(x))/dx
For example:
y=cos(x^2)
dy/dx=d(cos(x^2))/d(x^2) * d(x^2)/dx
dy/dx=-sin(x^2) * 2x
The differential is: dy = - 2xsin (x ^ 2) DX
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