Partial Derivative or Partial Differentiation

    

     1. What is a partial derivative?
2. Functions of two variables
3. Limits of functions of two variables
4. Continuity of functions of two variables

• Partial derivative definition
• Partial derivative notation
• Partial derivative symbol
• Partial derivative example

So, you can find answers to the following questions

·        Partial derivative definition:

In differential calculus, a partial derivative is defined as the derivative of a multivariable function with respect to one of its variables with all other variables held constant.

·      Partial derivative notation or symbol :

Partial derivatives is denoted by the symbol ∂.

·       What is ∂ called?

• How to  pronounce ∂?
• It may be pronounced as "partial dee", "doh"
• The partial derivative of a function f with respect to  x is variously denoted by  f_x, or ∂f/∂x. 

 

•  What is partial derivative example?

 

·        partial derivative examples

• For example: Let  f be  a function of  x and y then it will be expressed by f(x, y). Then, the partial derivative of the function  f with respect to x will be ∂f/∂x keeping the variable  y as constant. It is denoted that by  ∂f/∂x is also known as f_x

 

 

Functions of two variables

You know about function of one variable like f(x) = 2x

Now,

·        Can a function have two  variables ?

·        Yes, a function can have two variables also.

·      For example : f(x,y) = 2xy

·      How to  write a function with two variables?

 

 

3.   Limits of functions of two variables :

·       if the point (x,y) is close to the point (x0,y0) then f(x,y) is  close to the limit value  L

 

 

4.continuity of functions of two variables

·      How can you find the continuity of a function with two variables?

·      A function of two variables is continuous function at a point,

1.if the limit exists at that point, the function exists at that point

2.  And the limit and function are equal to the value of that function at that point.