Mathematical derivative formula? The basic formula for mathematical derivatives

The basic formula for derivatives: y = c (c is constant) y'=0、y=x^ny'=nx^（n-1）。

No, 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.

For the derivative function f(x), x f'(x) is also a function called a 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, derivation is a process of finding the limit, and the four rules of operation of derivatives are also the same as the four rules of operation of the limit.

Nature of Derivatives:

1) If the derivative is greater than zero, it increases monotonically; If the derivative is less than zero, it decreases monotonically; A derivative equal to zero is a stationary point of the function, not necessarily an extreme point. It is necessary to substitute the values on the left and right sides of the settlement point to find the positive and negative derivatives to judge the monotonicity.

2) If the function is known to be an increasing function, the derivative is greater than or equal to zero; If the function is known to be decreasing, the derivative is less than or equal to zero.

If the derivative of a function is greater than zero (or less than zero) in a certain interval, then the function increases monotonically (or decreases monotonically) in this interval, which is also called the monotonic region of the function.

A point where the derivative is equal to zero is called the balance of the function, at which the function may achieve a maximum or minimum (i.e., an extreme suspicious point). To make further judgments, you need to know the symbol where the derivative function is nearby. For a satisfying point, if there is such that both are greater than or equal to zero in the previous interval and less than or equal to zero in the subsequent interval, then it is a maximum point, and vice versa, it is a minimum point.

Here are the 16 basic derivative formulas 1:1The derivative of a constant function is the power function of its exponential multiplied by an exponential minus exponential function of $x$, and the derivative of an exponential function is itself multiplied by the base of the natural logarithm.

4.The derivative of a logarithmic function is the product of the reciprocal of its independent variable and the base of the natural logarithm. 5.

The derivative of the sine function is the cosine function. 6.The derivative of the cosine function is a negative sine function.

7.The derivative of the tangent function is the reciprocal of the difference between its square and 1, i.e., the square of the secant function. 8.

The derivative of the cosecant function is the opposite of the reciprocal of the difference between its square and 1, i.e., the opposite of the square of the cosecant function. 9.The derivative of the arcsine function is the opposite of the square root of the square of the difference of the 1 variable.

10.The derivative of the inverse cosine function is the opposite of the square root of the square of the difference of the independent variable and the difference of 1. 11.

The derivative of the arctangent function is the reciprocal of the square of its arguments and the sum of 1. 12.The derivative of the inverse cotangent function is the reciprocal of the square of its independent variable and the difference of 1.

13.The derivative of a hyperbolic sinusoidal function is its own derivative. 14.

The derivative of the hyperbolic cosine function is its own derivative. 15.The derivative of the hyperbolic tangent function is the reciprocal of the difference between its square and 1.

16.The derivative of the hyperbolic cotangent function is the opposite of the reciprocal of the difference between its square and 1. <>

Eight formulas: y=c (c is constant) y'=0；y=x^n y'=nx^(n-1)；y=a^x y'=a^xlna y=e^x y'=e^x；y=logax y'=logae/x y=lnx y'=1/x ；y=sinx y'=cosx ；y=cosx y'=-sinx ；Bending die y=tanx y'=1/cos^2x ；y=cotx y'=-1/sin^2x。

Algorithm: Addition (subtraction) rule: [f(x)+g(x)].'f(x)'+g(x)'

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

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

24 basic derivative formulas.

1. c = 0 (c is a constant).

2、（x∧n)′=nx∧(n-1)

3、(sinx)′=cosx

4、(cosx)′=sinx

5、(lnx)′=1/x

6、(e∧x)′=e∧x

7、(logax)'=1/(xlna)

8、(a∧x)'=a∧x)*lna

9、（u±v)′=u′±v′

10. (uv) = u v+uv surplus.

11、(u/v)′=u′v-uv′)/v

12. (f(g(x)) f(u)) g(x)) u=g(x)13, y=c(c is constant) y'=0

14、y=x^n y'=nx^(n-1)

15、y=a^x y'=a^xlna

y=e^x y'=e^x

16、y=logax y'=logae/xy=lnx y'=1/x

17、y=sinx y'=cosx

18、y=cosx y'=-sinx

19、y=tanx y'=1/cos^2x20、y=cotx y'=-1/sin^2x21、y=arcsinx y'=1/√1-x^222、y=arccosx y'=-1/√1-x^223、y=arctanx y'=1/1+x^224、y=arccotx y'=-1 1+x 2 The basic derivative formula is: (lnx).'=1/x、(sinx)'=cosx、(cosx)'=sinx

Derivation is a method of mathematical calculations 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 incremental limb 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.

y=e^xy'=e^x；y=logaxy'=logae/x，y=inxy'=1/x；y=sinxy'=cosx；y=cosxy'=-sinx。

The basic formula for the operation of 1 derivative.

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

What does 2 derivative mean.

The derivative Qi Mo Zhen is a local property of the function. The derivative of a function at a point describes the rate of change of the function around that point. If 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 high-thickness curve represented by the function at that point.

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's position and cavity with respect to time is the instantaneous velocity of the object.

The formula for the derivative is:c'=0 (c is constant).

x^a)'=ax (a-1), a is constant and a≠0a x).'=a^xlna

e^x)'=e^x

logax)'=1 (XLNA), A>0 and A≠1LNX).'=1/x

sinx)'=cosx

cosx)'=sinx

tanx)'=secx)^2

secx)'=secxtanx

cotx)'=cscx)^2

cscx)'=csxcotx

arcsinx)'=1 (1-x 2)arccosx).'=1/√（1-x^2)

arctanx)'=1/(1+x^2)

arccotx)'=1/(1+x^2)

shx)'=chx

chx)'=shx

uv)'=uv'+u'v

u+v)'=u'+v'

u/)'u'v-uv')/2

The derivative of the law is the following:

Subtraction rule: (f(x)-g(x)).'f'(x)-g'(x) Addition rule: (f(x)+g(x)).'f'(x)+g'(x) Multiplication Law Department Rules:

f(x)g(x))'f'(x)g(x)+f(x)g'(x)

Division rule: (g(x) f(x))).'g'(x)f(x)-f'(x)g(x))/f(x))^2