What is a partial derivative ,geometrical interpretation of partial derivatives and also discuss some of its uses or advantages. Discuss the difference between simple and partial derivatives.please dont explain it with the help of figure or equation.
The thing about questions like this is that they are intended to test your
Originally Posted by m777
understanding of the concept, so how we can help you is unclear to me.
It would be a bad thing to give you our answers, because it is no use to
you if your teacher thinks you have an adequate understanding of partial
derivatives their use and relationship to ordinary derivatives if you don't:confused:
I am totally agree with you and you are right.i have little bit concept of all things which i mention in my question but i am not a confident person even some time i done right question but i think that is wrong actually maths is not my major subject i always hate maths( love biology and chemistry) but i have to choose math because of computer science which is now my major subject.And i never copy any thing which you people answer me i always take concept or just for matching the answers of the questions which i have done some time i cant understand the methods one thing i must say that almost all concepts of me specially of higher level maths were develop by you people and i am really thankfull to you.
Any how i post here what i understand about my question.
Partial derivatives: have many important uses in math and science. We shall see that a partial derivative is not much more or less than a particular sort of directional derivative. The only trick is to have a reliable way of specifying directions ... so most of this note is concerned with formalizing the idea of direction. This results in a nice graphical representation of what “partial derivative” means. Perhaps even more importantly, the diagrams go hand-in-hand with a nice-looking exact formula in terms of wedge products.
Partial derivatives are particularly confusing in non-Cartesian coordinate systems, such as are commonly encountered in thermodynamics.
Ø Some of it is because of the intrinsic complexity of having so many different variables to worry about.
Ø Some of it is because there is a lot of sloppy notation in the literature, notation that makes it difficult (if not impossible) to figure out what the symbols are supposed to mean. You can get away with a certain amount of sloppiness in Cartesian coordinates, but that often leads to bad habits. Lots of things that are true in Cartesian coordinates are not true in general.
Ø Partial derivatives are useful in vector calculus and differential geometry
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are useful in vector calculus and differential geometry
Geometrical interpretation of partial derivatives
Suppose the graph of z = f(x,y) . is the surface Consider the partial derivative of f with respect to x at a point (x0,y0).Holding y constant and varying x, we trace out a curve that is the intersection of the surface with the vertical plane y = y0.
The partial derivative fx(x0,y0) measures the change in z per unit increase in x along this curve. That is, fx(x0,y0) is just the slope of the curve at (x0,y0). The geometrical interpretation of fy(x0,y0) is analogous.
Simple Derivatives: The rate of change [slope] of a function at a point is the limiting value of its average slope over an interval including that point, as the width of the interval shrinks to zero