Question 1: How to find the vector cross product? D(a X b)/dt, where a and b are both vectors about t, I know that the result obtained by ordinary multiplication is a d(AXB)/dt= AX(dB/dt)+(dA/dt)XB.

It turned out to be a little troublesome.

Question 2: The law of multiplication can be deduced. Here, how to derive (1/v)? You mean 1/v takes the derivative of v?

Then it is V (- 1)

Derivation-1/v2,

If you want to continue to take the derivative of x or something,

Multiplied by dv/dx, it is V'

Get - 1/v2 *v '

Question 3: How to identify genuine and fake Colgate toothpaste? 1. Seal judgment. Authentic paste cover is mechanically bonded with two-point glue, smooth and regular; Fake paste covers are all glued by hand, with irregular seals, many "tails" or no glue at all.

2. Production batch number judgment. The batch number of the box cover of the real paper box is the same as the front 1 1 of the toothpaste tube tail number; The fakes don't match.

Question 4: Why should Lagrange constraints be added to the derivative part of Lagrange multiplier method, and then differentiate each variable to make it = 0? Then bring the obtained variables into the maximum value; Or minimum.

Question 5: Who can find this second derivative? Need an answer urgently! ! ! Seeking the God of Higher Mathematics 20 12 National Unified Examination for Postgraduates' Entrance; Mathematics Examination Outline; Mathematics-1 Examination Subject; Advanced Mathematics (56%), Linear Algebra (22%), Probability Theory and Mathematical Statistics (22%); Full score in the examination paper structure 150; and the examination time 180 minutes. 8 multiple-choice questions, 4 points for each question. ***32 points fill in the blanks with 6 small questions, 4 points for each small question, 24 points for solving 9 small questions (including proof questions), and 94 points for the concept and representation of advanced mathematical functions, limit and continuous examination content functions, boundedness, monotonicity, periodicity and parity of functions, composite functions, inverse functions, piecewise functions and implicit functions, and properties and graphs of basic elementary functions. Establishment of function relation: definition and properties of sequence limit and function limit, left and right limit of function, concepts and relationships between infinitesimal and infinitesimal, properties and comparison of infinitesimal, four operations of limit, two criteria for the existence of limit: monotone bounded criterion and pinch criterion, two important limits:, concept of function continuity, types of function discontinuity points, continuity of elementary function, and properties of continuous function on closed interval. The examination requires understanding the concept of function and mastering the expression of function, which will establish the functional relationship of application problems. Understand the boundedness, monotonicity, periodicity and parity of functions. Understand the concepts of compound function and piecewise function, and understand the concepts of inverse function and implicit function. Master the nature and graphics of basic elementary functions and understand the concept of elementary functions. Understand the concept of limit, the concepts of left limit and right limit of function and the relationship between the existence of function limit and left limit and right limit. Master the nature of limit and four algorithms. Master two criteria of limit existence, and use them to find the limit, and master the method of finding the limit by using two important limits. Understand the concepts of infinitesimal and infinitesimal, master the comparison method of infinitesimal, and find the limit with equivalent infinitesimal. Understanding the concept of function continuity (including left continuity and right continuity) will distinguish the types of function discontinuity points. 10. Understand the properties of continuous function and continuity of elementary function, understand the properties of continuous function on closed interval (boundedness, maximum theorem, mean value theorem), and apply these properties. Concepts of derivative and differential, geometric meaning and physical meaning of derivative, relationship between derivability and continuity of function, tangent and normal of plane curve, four operations of derivative and differential, derivative of basic elementary function, differential method of function determined by compound function, inverse function, implicit function and parameter equation, higher derivative, invariance of first-order differential form, differential mean value theorem, Lobida's law, discrimination of monotonicity of function, extreme value of function, and discrimination of function graph. The examination requires understanding the concepts of derivative and differential, the relationship between derivative and differential, the geometric meaning of derivative, finding the tangent equation and normal equation of plane curve, and understanding the physical meaning of derivative. Master the four algorithms of derivative and the derivative rule of compound function, and master the derivative formulas of basic elementary functions and other functions. Knowing the four algorithms of differential and the invariance of first-order differential form, we can find the differential of function. If you understand the concept of higher derivative, you will find the higher derivative of simple function. Can find the derivative of piecewise function, derivative of implicit function, function determined by parameter equation, inverse function. Understand and apply Rolle theorem, Lagrange mean value theorem and Taylor theorem, and understand and apply Cauchy mean value theorem. Master the method of finding the limit of infinitive with L'H?pital's law. Understand the concept of extreme value of function, master the methods of judging monotonicity of function and finding extreme value of function with derivative, and master the methods and applications of finding maximum and minimum value of function. The concavity and convexity of the function graph will be judged by the derivative (note: in the interval (a, b), let the function f(x) have the second derivative, at this time, the graph of f(x) is concave; At that time, the graph of f(x) was convex), the inflection point and horizontal, vertical and oblique asymptotes of the function graph were found, and the function graph was depicted. Understand the concepts of curvature, curvature circle and curvature radius, and calculate curvature and curvature radius. Concepts of primitive function and indefinite integral, basic properties of indefinite integral, basic >>