Deriving a Function of Two Variables

[brollysan]

Derivating a function of a function with two variables

Hi i am new to this forum so please bear with me if i made a mistake or posted in the wrong section :)

Homework Statement

Given that f(x,y)= ((x^-1)+(y^-1)) find F'x and F'y
Given z= F(x,y) and x=f(t) while y= g(t,s) express dz/dt and dz/ds

Homework Equations

This i hope you can help me with, missed the lecture where the professor explained this and i can't find any relevant information in the math book nor did googling or wikipedia help.

The Attempt at a Solution

This is the first time i encounter derviation of functions, I have no problems derivating equations and most of my life i just had to derivate X, this is why i have no clue as to how i should solve this problem.

F'x= -1/(x)^2 and F'y= -1/(y)^-2

I hope you can explain it to me instead of just giving an answer and i will be grateful.


Thanks for your help and sorry for the bad english

Edit: Even the name of the subject this problem touches would be ok, and hopefully some links :D more fun that way

 

[HallsofIvy]

Hi i am new to this forum so please bear with me if i made a mistake or posted in the wrong section :)

Homework Statement

Given that f(x,y)= ((x^-1)+(y^-1)) find F'x and F'y
Given z= F(x,y) and x=f(t) while y= g(t,s) express dz/dt and dz/ds

Homework Equations

This i hope you can help me with, missed the lecture where the professor explained this and i can't find any relevant information in the math book nor did googling or wikipedia help.

The Attempt at a Solution

This is the first time i encounter derviation of functions, I have no problems derivating equations and most of my life i just had to derivate X, this is why i have no clue as to how i should solve this problem.

F'x= -1/(x)^2 and F'y= -1/(y)^-2

I hope you can explain it to me instead of just giving an answer and i will be grateful.


Thanks for your help and sorry for the bad english

Edit: Even the name of the subject this problem touches would be ok, and hopefully some links :D more fun that way

You are dealing with partial derivatives since F depends upon two independent variables.
What you are calling "F'x" and "F'y" would be more properly called \partial F/\partial x and \partial F/\partial y or just F_x and F_y, respectively.

The partial derivative of a function, with respect to x, is jus the derivative treating y as a constant. What is dF/dx if F(x)= x^-1+ C for some constant C? What is dF/dy if F(y)= C+ y^-1?

 

[brollysan]

Thank you so much, i am going to try and find relevant information on this subject and learn it by myself :) thanks again. I will solve the querstions you asked in a few hours, have to eat first.

 

[brollysan]

Allright for the second part of the problem i have that z = F(x,y)= F(f(t), g(t,s))

I understand that dz/dt= F'x(x,y)dx/dt + F'y(x,y)dy/dt

But what about dz/ds, how do i proceed there?

Edit:

seeing as s isn't a function of f(x)=x is x a constant when you derivate dz/ds? If x is a constant, would the correct answer be

dz/ds= F'y(x,y)(dy/ds)?

 

[eys_physics]

Hey
Yes it is correct. As x has no dependence on s
\frac{\partial{x}}{\partial{s}}=0

 

[brollysan]

Thank you :)

Edit: How do you guys manage to write the symbols in here? Html code?