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**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 :)

**1. 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

**2. 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.

**3. 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

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