Extending the original formula, because it is an integral of t and x in (x-t) is a constant, it can be put forward that ∫ (0, x) (x-t) f (t) dt = x ∫ (0, x) f (t) dt-∫ (0, x) T.

Derivation is a calculation method in mathematical calculation, and its definition is the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable.

A term in mathematics, that is, to derive a function and use it.

Basic derivative formula

Give the increment of the independent variable;

Obtain the function increment;

Doing business;

Seek the limit.

Logarithmic derivative rule

Function is called power exponential function, which will be involved in a large number of economic activities and is very special. It is neither an exponential function nor a power function, and its power base and exponent have independent variables X, so it cannot be treated by the differential method of elementary functions. This paper introduces a method to solve this kind of function-logarithmic derivative method.

Logarithms are taken on both sides (of course, it is more convenient to calculate the natural logarithm based on E). Using the operational properties of logarithm.

References:

Baidu encyclopedia-integral