### Properties of derivative

Functions: f, g, y, u, v

Argument (independent variable): x

Real constant: k

Angle: α

### 1. Derivative of a function:

The derivative of a function y=f(x) measures the rate of change of y with respect to x. Suppose that at some point x ∈ R, the argument of a continuous real function y=f(x) has an increment Δx . Then the increment of the function is equal to Δy = f(x+Δx)− f(x).

The derivative of a function y=f(x) at the point x is defined as the limit of the ratio

From a geometrical point of view, the derivative of a function y=f(x) at the point x is equal to the slope of the tangent line to the curve f(x) drawn through this point:

### 2. Derivative of the sum of two functions:

The derivative of the sum of two functions is equal to the sum of their derivatives:

### 3. Derivative of the difference of two functions:

The derivative of the difference of two functions is equal to the difference of their derivatives:

### 4. Constant factor:

A constant factor can be taken out of a derivative:

### 5. Derivative of the product of two functions:

### 6. Derivative of the quotient of two functions:

### 7. Derivative of a composite function (chain rule)

### 8. Derivative of an inverse function:

Where, x(y) is the inverse function for y(x)