e in the derivative formula, the derivative of e x

e is a constant, and like "pie" it is an infinite non-cyclic decimal, as if it were two points and a few points.

Just think of e as a constant, I don't talk about how to calculate it, but there are a lot of formulas for e in exponential logarithms, so e can be used directly.

e is also like a pie, several.

No problem.

e is the base of the natural logarithm, an infinite non-cyclic decimal, whose value is, is defined as follows:

When n->, (1+1 n) the limit of n.

Note: x y denotes x to the y power.

As n increases, the base gets closer and closer to 1, and the exponent tends to infinity, so does the result tend to 1 or infinity? Actually, it tends to be, if you don't believe it, use a calculator to calculate, and take n=1, 10, 100, 1000 respectively. However, since the general calculator can only display about 10 digits, it is impossible to see any more.

E is used a lot in science and technology, and generally does not use a logarithm with a base of 10. With e as the base, many formulas can be simplified, and it is the most "natural", so it is called "natural logarithm".

The derivative of e is 0, and the derivative of any constant (functional) number is 0.

Not all known functions have derivatives, and a function does not necessarily have derivatives at all points. If a function exists at a certain point in derivative, it is said to be derivable at that point, otherwise it is called underivable. However, the derivable function must be continuous; Discontinuous functions must not be derivative.

The function y=f(x) formula

When the function y=f(x) is an independent variable.

When x produces an incremental δx at a point x0, the ratio of the incremental omission δy of the output value of the function to the incremental δx of the independent variable is at the limit a when δx approaches 0, if it exists, a is the derivative at x0 and is denoted as f'(x0) or df(x0) dx.

Derivatives are local properties of functions. The derivative of a function at a point describes the rate of change of the function around that point. If both the independent variables and the values of the function are real, then the derivative of the function at a certain point is the tangent of the curve represented by the function at that point.

Slope. The essence of derivatives is to perform a local linear approximation of a function through the concept of limits. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.

Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If a function exists at a certain point in derivative, it is said to be derivable at that point, otherwise it is called underivable. However, the derivable function must be continuous; Discontinuous functions must not be derivative.

The calculation process is as follows:(e^-x)'

-x)'e^-x

e^-xThe basic derivative is as follows:1. Linearity of derivation: Derivation of linear combination of functions is equivalent to finding the derivative of each part of the function and then taking the linear combination (i.e., formula).

2. The derivative function of the product of two functions: one derivative multiplied by two + one by two derivative (i.e. formula).

3. The derivative function of the quotient of two functions is also a fraction: (sub-derivative mother-child multiplication mother) divided by the female square (i.e., formula).

4. If there is a composite function, the derivative is obtained by the chain rule.

-e^(-x)

Analysis: The derivative of e x is e x, and the derivative of -x is -1, so the composite function e (-x) derivative = -e (-x).Additional Information:Chain Rule:

If h(a)=f[g(x)], then h'(a)=f’[g(x)]g’(x)。

The law of chains is described in words as "a composite function made up of two functions, the derivative of which is equal to the derivative of the value of the inner function substituted by the outer function, multiplied by the derivative of the inner function." ”

Derivative formula for quotient:

u/v)'=u*v^(-1)]'

u' *v^(-1)] v^(-1)]'u= u' *v^(-1)] 1)v^(-2)*v' *u=u'/v - u*v'/(v^2)

It's easy to get.

u/v)=(u'v-uv')/v²

Common derivative formulas:

1、c'=0

2、x^m=mx^(m-1)

3、sinx'=cosx，cosx'=-sinx，tanx'=sec^2x

4、a^x'=a^xlna，e^x'=e^x5、lnx'=1/x，log(a,x)'=1/(xlna)6、(f±g)'=f'±g'

7、(fg)'=f'g+fg'

This is a nested function whose derivative is: e (-x) to the derivative of -x multiplied by the ...... of the derivative of -x to x

The specific answer of Hui Qinghu is as follows:Let's look at E Y as a whole A

The xy power of e is a x

a^x*lna

e^xy*lne^y

e^xy*y

i.e. y times e to the xy power.

Calculation of derivatives:The derivative function of a known function can be calculated according to the definition of the derivative using the limit of the change ratio, and in practice, most common analytic functions can be regarded as the sum, difference, product, quotient or composite result of some simple functions.

As long as we know the derivatives of these simple functions, we can deduce the derivatives of more complex functions according to the derivative law of derivative balance.

y‘=[e^(-x)]'

x)'*e^(-x)=-e^(-x)

Answer Analysis: Composite Functions.

Derivation – Derivation is sought first for the inner layer and then for the outer layer.

Extended Resources:Derivative formula for basic functions.

is constant) y'=0

y'=nx^(n-1)

y'=a^xlna

y=e^x y'=e^x

y'=logae/x

y=lnx y'=1/x

y'=cosx

y'=-sinx

y'=1/cos^2x

y'=-1/sin^2x

y'=1/√1-x^2

y'=-1/√1-x^2

y'=1/1+x^2

y'=-1/1+x^2

Derivative of the composite function: yx'=yu'×ux'

Take your question as an example:

y=e^-x

Let u=-x y=e u

y'=(e^u)'×(-x）'=e u (-1)=-e -xNote: The y in y=e -x in the question is the yxu in the formula = u, which is the ux in the formula, and the y in y=e u is the yu in the formula'=e^x】

The first derivative of -x is -1

Consider -x as a whole and then find the derivative, or replace -x with u, and the derivative of e u is e u = e -x, and 1 is multiplied by e -x.

e^-x

e^(1/x)]'e^(1/x)·x⁻²

For the derivative function f(x), x f'(x) is also a function called the derivative of f(x). The process of finding the derivative of a known function at a point or its derivative is called derivative. In essence, derivative is a process of finding the extreme sensitive bridge limit, and the four rules of operation of derivatives are also the four rules of operation of the limit.

e^(iπ)＝cosπ+isinπ＝-1。

e^(a+bi）=e^a×e^(bi)=e^a[cos(b)+i*sin(b)]。

Brief introduction. In mathematics, an imaginary number is a number of the form a+b*i, where a, b are real numbers, and b≠ is 0, i = 1. The term "Void Eggplant Number" was coined by the famous mathematician Descartes in the 17th century, because the concept at the time was that it was a number that did not really exist.

Later, it was found that the real part a of the imaginary number a+b*i corresponds to the horizontal axis of the lead state on the plane, and the imaginary part b corresponds to the vertical axis on the corresponding plane, so that the imaginary number a+b*i can correspond to the points (a, b) in the plane.

The imaginary number bi can be added to the real number a to form a complex number of the form a + bi, where the real numbers a and b are called the real and imaginary parts of the complex number, respectively. Some authors use the term pure imaginary number to denote the so-called imaginary number, which denotes any complex number with a non-zero imaginary part.