## How to solve Derivatives

# Derivatives theory

Derivatives: It is called numerical function to any application of a set E in R

For the determination of a function is necessary to know three conditions:

- The initial set
- The final set
- Establish a rule that allows us to associate to each element of the initial set a single element of the final set

Notations:

– The initial set is called the domain of definition or field of existence of the function.

– Each element of the initial set is called independent variable.

– The number y associated by the function f (x) is called the dependent variable.

– It is called a graph of a function to the set of the images of the independent variable

Tangent line equation:

The slope of the tangent to a curve at a point is equal to the derivative of the function at that point

Normal line equation:

The normal line of a curve y = f (x) at a point x_{0} is that which passes through the point and whose slope is equal to the inverse of the opposite of f ‘(a).

**DERIVATIVE OF A FUNCTION AT A POINT**

The derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative

can be thought of as how much one quantity is changing in response to changes in some other quantity;

for example, the derivative of the position of a moving object with respect to time is the object’s instantaneous velocity.

The function of f derived is that so each element x does it match the derivative of the function at that point. This function is denoted by f ‘(x).

Applying the formula of the derivative, we can calculate the derivative of any function. For convenience we use the following summary of the derivatives of the most common functions, which allows us to do the same without resorting to the definition in each case.

**DERIVATIVES OF ELEMENTARY FUNCTIONS:**

**RATIONAL FUNCTIONS**

**METHOD OF THE LOGARITHMIC DERIVATION**

It is very useful in case of products quotients or powers of functions

Steps to take:

1º Logarithms are placed in the expression

2º The function is derived

3º Solve the equation for y’

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