What is a function? What are the functions? What is the natural logarithm? What is a function? What are the functions? What is the natural logarithm? What is the exponent? How to find the natural logarithm and exponent? Don't say something useless!

In mathematics, a function is a relationship in which each element in a set corresponds to a unique element in another (possibly identical) set
Functions include:
Composite function:
There are three variables, y is the function of u, y = ψ (U), u is the function of X, u = f (x), which can often form a chain: y forms the function of X through the intermediate variable U
If u * & Iacute; u, F and ψ form a composite function, such as y = lgsinx, X ∈ (0, π). In this case, SiNx ＞ 0, lgsinx is meaningful. But if x ∈ (- π, 0), SiNx ＜ 0, lgsinx is meaningless, it cannot be a composite function
Inverse function
Let y = f (x) be a known function. If for each Y ∈ y, there is a unique x ∈ x such that f (x) = y, this is a process of finding x from y, that is, X becomes a function of Y, denoted as x = f - 1 (Y). F - 1 is called the inverse function of F. it is customary to use X to represent the independent variable, so this function is still denoted as y = f - 1 (x), For example, y = SiNx and y = arcsinx are inverse functions of each other. In the same coordinate system, the graphs of y = f (x) and y = f - 1 (x) are symmetric with respect to the line y = X
Implicit function
If the function y = f (x) is determined by the function equation f (x, y) = 0, that is, f (x, f (x)) ≡ 0, then y is said to be the implicit function of X
Multivariate function
Set point (X2,..., x1,...) , xn) ∈ G & Iacute; RN, u & Iacute; R1, if for every point (x1, X2 For a rule F, there is a unique u ∈ u corresponding to F: G → u, u = f (x1, X2 , xn), then f is called an n-ary function, G is the domain of definition, and u is the range of values

What function's derivative is based on the natural logarithm, the logarithm of X

∫lnxdx
=xlnx-∫xdlnx
=xlnx-∫x*1/x dx
=xlnx-∫dx
=xlnx-x+C

In the logarithmic derivation method, why is the natural logarithm ln taken on both sides of the function instead of the commonly used logarithm LG or other logarithm log?

Because the derivative of natural logarithm is the simplest: (LNX) '= 1 / X
The derivative of the common logarithm or other logarithms also contains a factor: 'loga (x)]' = 1 / (xlna)
Although both can be used, the former is more concise

What is a function? What are the functions? What is the natural logarithm? What is a function? What are the functions? What is the natural logarithm? What is the exponent? How to find the natural logarithm and exponent? Don't say something useless!