Mathematical derivative formula of senior two
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2. Derivative relationship between the original function and the inverse function (the inverse trigonometric function is derived from the derivative of trigonometric function): If the inverse function of y=f(x) is x=g(y), then there is y'= 1/x'.
3. Derivative of composite function:
The derivative of the compound function to the independent variable is equal to the derivative of the known function to the intermediate variable, multiplied by the derivative of the intermediate variable to the independent variable-called the chain rule.
4. The integral derivative rule:
(a(x), b(x) is a subfunction)
Calculation of derivative
The derivative function of a known function can be calculated by using the limit of change rate according to the definition of derivative. In practical calculation, most common analytic functions can be regarded as the result of sum, difference, product, quotient or mutual compound of some simple functions. As long as the derivative functions of these simple functions are known, the derivative functions of more complex functions can be calculated according to the derivative law.
Derivation rule of derivative
Deduction rule
The derivative function of a function composed of the sum, difference, product, quotient or mutual combination of basic functions can be derived from the derivative rule of the function. The basic deduction rules are as follows:
Linearity of derivative: To find the linear combination of derivative functions is equivalent to finding the derivatives of each part first and then finding the linear combination.
The derivative function of the product of two functions, one derivative multiplied by two+one derivative multiplied by two.
The derivative function of the quotient of two functions is also a fraction. (derivative times mother-derivative times mother) divided by mother.
Derivation rule of compound function
If there is a compound function, if you need the derivative of the function at a certain point, you can first find the derivative function of this function by the above method, and then you can see the value of the derivative function at this point.
higher derivative
Solution of higher derivative
1. Direct method: Find the higher derivative step by step from its definition.
Generally used to find solutions to problems.
2. The algorithm of higher derivative:
(binomial theorem)
3. Indirect method: using the known higher-order derivative formula, through four operations, variable substitution and other methods.
Note: the function after substitution should be easy to find, and try to get the order derivative as close as possible to the known formula.
Senior two mathematics derivative foundation test center.
Test center 1: Derive the formula.
Example 1. F(x) is the derivative function of f(x) 13x2x 1, so the value of f( 1) is 3.
Test site 2: the geometric meaning of derivative.
Example 2. It is known that the tangent equation of the image of function yf(x) at point m (1, f( 1)) is y.
1x2 and then f( 1)f( 1) 2.
The tangent equation at 3) is Example 3. The curve yx32x24x2 is located at the point (1
Comments: The above two small questions are all about the geometric meaning of derivatives.
Test site 3: the application of derivative geometric meaning.
Example 4. Given curve C: YX33x22x and straight line l:ykx, straight line l is tangent to curve c at points x0 and x0, y0x00, find the equation and tangent coordinates of straight line l. ..
Comments: This little question examines the application of derivative geometric meaning. What should we pay attention to in solving this kind of problem? Is the tangent point on both the curve and the tangent? The application of this condition. The differentiability of a function at a certain point is a sufficient condition for the existence of a tangent at that point on the corresponding curve, but it is not a necessary condition.
Test site 4: monotonicity of function.
Example 5. It is known that fxax3xx 1 is a decreasing function on r, and the range of a is found. 32
Comments: This topic examines the application of derivatives in monotonicity of functions. For the monotonicity problem of higher-order functions, we should have the consciousness of derivative.
Test site 5: extreme value of function.
Example 6. Let the function f(x)2x33ax23bx8c take extreme values at x 1 and x2.
(1) Find the values of a and b;
(2) For any maximum and minimum on x,