The problem of capture derivative of the set function is basic both for pupils of high schools, and for students of higher educational institutions. It is fully impossible to master a mathematics course without assimilation of a concept of a derivative. But you should not be frightened ahead of time - any derivative can be calculated using the simplest algorithms of differentiation and knowing derivatives of elementary functions.
It is required to you
- Table of derivative elementary functions, rules of differentiation
Instruction
1. By definition of derivative function the relation of increment of function to increment of an argument for an infinitesimal period is. Thus, the derivative shows dependence of growth of function on change of an argument.
2. To find a derivative of elementary function it is enough to use the table of derivatives. The full table of derivative elementary functions is provided on the drawing.
3. To find the derivative sum (differences) of two elementary functions we use the rule of differentiation of the sum: the derivative of the sum of functions is equal to the sum of their derivatives. It registers as: (f (x) +g(x)) '=f' (x) +g' (x). Here (') capture derivative of function is shown a symbol. And further the task comes down to capture of derivative two elementary functions, described on the previous step.
4. To find a derivative of performing two functions, it is necessary to use one more rule of differentiation: (f (x) *g(x)) '=f' (x) *g(x)+f (x) *g' (x), that is the derivative of the work is equal to the sum of the work of a derivative of the first multiplier on the second and first a multiplier on a derivative of the second. It is possible to find a derivative private on the formula presented on the picture. It is very similar to the rule of capture of a derivative of the work, only instead of the sum in numerator there is a difference, and the denominator in which there is a square of a denominator of the set function is added.
5. Capture of derivative difficult function - the most difficult task at differentiation (difficult function is called function which argument is any dependence). But also it is solved on quite simple algorithm. At first we take a derivative on a difficult argument, including its simple. Then we multiply the received expression by a derivative of a difficult argument. So we can find a function derivative with any degree of enclosure.