Math Is Fun Forum

Silvia

Novice

From: Sao Paulo

Registered: 2023-06-09

Posts: 2

Partial Derivatives

my query is:

Given a function F(x,y)=A*x*x*y, calculate dF(x,y)/d(1/x), to calculate this derivative I make a change of variable, let u=1/x, then the function becomes F(u,y)=A*(1/u*u)*y, calculating the derivative with respect to u, we have dF/du=-2*A*y*(1/(u*u *u)) replacing we have dF/d(1/x)=-2*A*x*x*x*y
On the other hand, if we create the same original function, but as a function of (1/x), F(x,y)=A*(1/x)*(1/x)*x*x*(x*x) *y we derive with respect to (1/x) we have dF/d(1/x)= A *x*x*x*y Why are different results obtained?.  Maybe I am wrong in something simple, but fundamental. Could you help me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,199

Re: Partial Derivatives

hi Silvia

Welcome to the forum.

Your first method is correct and agrees with what I got

The second won't work because the x terms on the numerator are functions of 1/x and therefore have to be part of the (partial) differentiation process.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Silvia

Novice

From: Sao Paulo

Registered: 2023-06-09

Posts: 2

Re: Partial Derivatives

Thanks for answering Silvia.