Differentiation (finding of derivative function) - the most important task of the mathematical analysis. Finding of derivative function helps to investigate properties of function, to build its schedule. Differentiation is applied at the solution of many problems of physics and mathematics. How to learn to take derivatives?
It is required to you
- Table of derivatives, notebook, handle
Instruction
1. Learn definition derivative. In principle, it is possible to take a derivative and without knowing definition of a derivative, but understanding of the events at the same time will be insignificant small.
2. Make the table of derivatives in which write down derivatives of the main elementary functions. Teach them. Just in case you hold the table of derivatives always near at hand.
3. Look whether it is possible to simplify the presented function. In certain cases it considerably facilitates capture of a derivative.
4. The derivative of constant function (constant) is equal to zero.
5. Rules of differentiation (rules of finding of a derivative) are output from definition of a derivative. Learn these rules. The derivative of the sum of functions is equal to the sum of derivative these functions. The derivative of a difference of functions is equal to the difference of derivative these functions. The sum and a difference can be united under one concept of the algebraic sum. The constant multiplier can be taken out for the sign of a derivative. The derivative of performing two functions is equal to the sum of works of derivative first function on the second and derivative second function on the first. The derivative of private two functions is equal: the derivative of the first function to increase minus by the second function the derivative of the second function to increase by the first function, and to divide all this into a square of the second function.
6. To take a derivative of difficult function, it is necessary to present consistently it in the form of elementary functions and to take a derivative by the known rules. It is necessary to understand that one function can be an argument of other function.
7. Consider the geometrical meaning of a derivative. The function derivative in a point x is a tangent of angle of an inclination of a tangent to a function graph in a point x.
8. Practice. Begin with finding of a derivative of simple functions, then you pass to more difficult.