To deduce a noun in mathematics is to deduce a function. Find the derivative of the function y=f(x) at x0 by the derivative method (1) represented by ()': ① Find the function δ y = f (x0+δ x)-f (x0) ② Find the average change rate ③ Take the limit and find the derivative. (2) Derivation formulas of several common functions: ① C'=0(C is a constant); ②(x^n)'=nx^(n- 1)(n∈q)； ③(sinx)' = cosx； ④(cosx)' =-sinx； ⑤(e^x)'=e^x； ⑥ (a x)' = a A Xin (ln is a natural logarithm) (3) Four algorithms of derivatives: ① (Uv)' = Uv' ② (UV)' = Uv+UV' ③ (U/V)' = (Uv-UV'. Derivative is an important pillar of calculus! Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications. Calculus is based on real numbers, functions and limits. The most important idea of calculus is to use "infinitesimal" and "infinite approximation", just like a thing is always changing, and you can't learn it well, but if you divide it into small pieces with infinitesimal, you can think of it as continuous processing and finally add it up. Calculus is a general term for differential calculus and integral calculus. It is a mathematical idea, in which' infinite subdivision' is differential and' infinite summation' is integral. Infinity is the limit, and the thought of limit is the basis of calculus, that is, to look at problems with a moving thought. For example, the instantaneous speed of a bullet flying out of a gun bore is the concept of differentiation, and the sum of the distances traveled by a bullet at each instant is the concept of integration. If the whole mathematics is compared to a big tree, then elementary mathematics is the root of the tree, each branch of mathematics is the branch, and the main part of the trunk is calculus. Calculus is one of the greatest achievements of human wisdom. The concepts of limit and calculus can be traced back to ancient times. In the second half of the 17th century, Newton and Leibniz completed the preparatory work that many mathematicians participated in, and independently established calculus. Their starting point of establishing calculus is intuitive infinitesimal, and their theoretical foundation is not solid. It was not until the19th century that Cauchy and Wilstrass established the limit theory, and Cantor and others established the strict real number theory that the discipline was rigorous. Calculus is developed with practical application, and is more and more widely used in various branches of natural science, social science and applied science such as astronomy, mechanics, chemistry, biology, engineering and economics. In particular, the invention of computers is more conducive to the continuous development of these applications. Everything in the objective world, from particles to the universe, is always moving and changing. Therefore, after introducing the concept of variables into mathematics, it is possible to describe the movement phenomenon in mathematics. Due to the emergence and application of the concept of function and the needs of the development of science and technology, a new branch of mathematics has emerged after analytic geometry, which is calculus. Calculus plays a very important role in the development of mathematics. It can be said that it is the greatest creation in all mathematics after Euclidean geometry. See more calculus/view/view/3139.htm.