How do you calculate the derivative? How are derivatives calculated?

Look at the book, it's very simple. For example, the derivative of y to the fourth power is equal to the power of 4*y. Multiply 4 to the front, then drop it once.

1) Steps to find the derivative of the function y=f(x) at x0: Find the increment of the function δy=f(x0+δx)-f(x0) Find the average rate of change Take the limit and get the derivative.

2) Derivative formulas for several common functions.

3) The Four Rules of Algorithm for Derivatives.

3) Composite functions.

Derivative of the independent variable.

Summarize according to the textbook as described above.

The derivative is very simple, summarize the formula in the book, and then apply it...

I think that in the college entrance examination, the derivative is not the difficulty.

It mainly relies on the derivative formula. Simple functions are directly substituted into formulas, and composite functions have to be split into simple functions and calculated step by step. Read more books, it's simple.

There are several basic formulas for reciprocal counts, such as the cube of x = 3 * the square of x, and so on.

Need to read the book.

This problem cannot be completed in a few words, if you have the attitude to learn this well, you will forget it by self-study.

I think derivatives are supposed to be in high school, can you be specific? Send it over and try to help you out.

If there is a formula, you can find it on the Internet yourself! Bring it in and forget it!

1. Definition of utilization.

2. The derivative formula is mainly used.

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

The formula for the four rules of operation of derivatives is as follows:

The law of addition (subtraction): [f(x)+g(x)].'f(x)'+g(x)'。

Multiplication: [f(x)*g(x)].'f(x)'Disturbance *g(x)+g(x).'*f(x)。

Division rule: [f(x) g(x)].'f(x)'*g(x)-g(x)'*f(x)]/g(x)^2。

Usage of Derivative Formula:

A function does not necessarily have derivatives on all point curvatures. 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) is the derivative f of the buried Li He at the x0 point'The geometric meaning of (x0): represents the slope of the tangent of the function curve at the point p0(x0,f(x0)) (the geometric meaning of the derivative is the tangent slope of the function curve at this point).

The above content reference: Encyclopedia - Derivative.

1. Use the definition to make a reputation.

2. The derivative formula is mainly used.

is constant) y'=0

y'=nx^(n-1)

y'=a^xlna

y=e^x y'=e^x

y'=logae oak x

y=lnx y'Vernal = 1 x

y'=cosx

y'=-sinx

Let the function y=f(x) be defined in a certain neighborhood of the point x0, and when the independent variable x has an increment δx at x0, and (x0+δx) is also in this neighborhood, the function accordingly obtains the delta δy=f(x0+δx)-f(x0); If the ratio of δy to δx exists when δx 0, then the function y=f(x) is said to be derivative at point x0, and this limit is called the derivative of the function y=f(x) at point x0, denoted as y=f'(x).

Second, to find the derivative correctly, you must first remember the derivatives of the 14 basic elementary functions, as well as the multiplication, addition, and division of derivatives, as shown in the figure below.

Seek a way to repent.

Find the increment of the function δy = f(x0 + δx)-f(x0) find the average rate of change and take the derivative of the limit. c'Hall shout = 0 (c is a constant function) (x n).'=nx (n-1) (n r) memorize the derivative of 1 x.

sinx)' cosx

Derivative, also known as derivative value. Also known as micro-quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) produces an incremental δx at a point x0, the ratio of the incremental 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.

If the stool is used to derive the indefinite integral formula f(x)dx, then the result is f(x), and if it is an equation like f(x-t)dx, it is necessary to convert the integral variable first, and then find the derivative of the jujube family.

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, the derivative of the function at a point is the tangent slope of the curve represented by the function at that point.

The details are 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 the derivatives of these simple functions are known, the derivatives of more complex functions can be deduced according to the derivative law of derivatives.

Definition of derivative.

Let the function y=f(x) be defined at and near the point x=x0 as an independent variable.

x has a change of amount x at x0 ( x can be positive or negative), then the function y has a corresponding change of y=f(x0 x) f(x0), and the ratio of these two changes is called the average rate of change of the function y=f(x) between x0 and x0 x.

If there is a limit when x 0, we say that the function y=f(x) is derivative at the point x0, and this limit is called the derivative of f(x) at the point x0 (i.e., the instantaneous rate of change), denoted as f(x0) or, i.e.

The derivative of the function f(x) at the point x0 is the limit of the mean rate of change of the function when the amount of change of the independent variable tends to zero If the limit does not exist, we say that the function f(x) is not derivable at the point x0.

2. The method of finding the derivative.

Defined by the derivative, we can get the method of finding the derivative of the function f(x) at the point x0:

1) Find the increment of the function y=f(x0 x) f(x0);

2) find the average rate of change;

3) Take the limit and get the derivative.

3. The geometric meaning of derivatives.

The geometric meaning of the derivative of the function y=f(x) at the point x0 is believed to be the slope of the tangent of the curve y=f(x) at the point p(x0,f(x0)).

Correspondingly, the tangent equation.

is y y0=

f′(x0)(x－x0).

4. Derivatives of several common functions.

The derivative of the function y=c (c is a constant).

c′=0.The derivative of the function y=xn(n q).

xn)′=nxn－1

The derivative of the function y=sinx.

sinx)′=cosx

Derivative of the function y=cosx.

cosx)′=sinx

5. Derivation of the four rules of function.

and the derivative. u＋v)′=u′＋v′

Bad derivative. u－v)′=

The derivative of the product of u v.

u·v)′=u′v＋uv′

Derivative of quotient. 6. Composite functions.

The law of derivation.

In general, the derivative y x of the composite function y=f[(x)] to the independent variable x is equal to the derived y u of the known function to the intermediate variable u= (x), and the key wheel is multiplied by the derivative u x of the intermediate variable u to the independent variable x, i.e., y x = y u·u x

7. Logarithmic and exponential functions.

Derivatives of . 1) Logarithmic functions. Derivatives of .

The formula cannot be entered.

where Eq. (1) is a special case of Eq. (2), and when A=E, Eq. (2) is Eq. (1).

2) The derivative of the exponential function.

ex)′=ex

ax)′=axlna

where Eq. (1) is a special case of Eq. (2), and when A=E, Eq. (2) is Eq. (1).

The derivative, also known as the microquotient, is the differentiation quotient of the dependent variable and the differentiation of the independent variable; Integrating the derivative gives you the original function (which is actually the sum of the original function and a constant).