Derivative of integral equation 5, how to find the derivative formula of integral?

The formula for finding the integral is: f(x) =a,x) xf(t) dt.

f'(x) =a,x) f(t) dt + x * x' *f(x) -a' *f(a)]

1 x)f(x) +x * 1 * f(x) -0 * f(a)] (the derivative of the lower bound a is 0, so the whole will become 0).

1/x)f(x) +xf(x)

The integral variable upper bound function and the integral variable lower bound function are collectively referred to as the integral variable limit function, which are generally converted into variable upper bound integral derivatives when calculating the derivative. If the function f(x) is continuous over the interval [a,b], then the integral variable upper bound function has a derivative on [a,b].

If the function f(x) is continuous over the interval [a,b], then the first search of the integral variable upper bound function is a primitive function of f(x) on [a,b].

If the upper limit x changes arbitrarily over the interval [a,b], then for each given value of x, the definite integral has a corresponding value, so it defines a function on [a,b], which is the integral limiting Qichun function.

Integral variable limit functions are an important class of functions, and their most famous application is in the proof of Newton's Leibniz formula. In fact, the integral variable limit function is an important tool for generating new functions, especially because it can represent non-elementary functions and transform integral problems into differential problems.

In addition to expanding our understanding of the concept of functions, integral variable limit functions have important applications in many occasions.

The process of deriving the definite integral is as follows:

Derivative is a mathematical method of calculation that is defined as the limit of the quotient between the increment of the dependent variable and the increment of the independent variable when the increment of the independent variable tends to zero. When there is a derivative of a function, it is said to be derivable or differentiable. The derivable function must be continuous.

Discontinuous functions must not be derivative.

<> don't know if you're trying to find a guide from f to r.

Example: Select x as the derivative and e x as the original function, then.

integral = xe x-se xdx = xe x-e x+c

Generally, you can use the partial integration method: The form is like this: Integral: u(x)v'(x)dx=u(x)v(x)-integral: u'(x)v(x)dx integrand.