Question

I'm not quite really understanding the multivariable chain rule. Can someone please explain to me why you multiply by the partials derivatives? Thanks

Answer 1

you will only get to understand the chain rule(both for single-var and multi-var calculus) after you're done with introduction to analysis
until then there is no way to show any proof whatsoever

Answer 2

Awws :(

Answer 3

Thanks for posting this. I know I can know rest until I do analysis.

Answer 4

I am not sure what you need: the reason / proof? or how to do the chain rule? Who cares about the proof, right? To do the chain rule, just take the partial derivative of each term. This will give you a new equation for each number of terms (2 variables result in 2 new equations / derivatives etc...). Next, just fill in for the variables of each partial deriv. using the given terms of (t), then mutliply each equation by the deriv of each given. That's pretty much it.

Ex: Let f(x,y) = \[x^{2}-y^{2}\] and x(t) = cos(t) and y(t) = sin(t)

Find: d/dx f[x(t), y(t)]

f(x,y)= 2x-2y dx/dt = -sin(t), dy/dx = cos(t)

put it all together
1. multiply the dx/dt and dy/dt terms by the f(x,y):

= -2xsin(t) - 2ycos(t)

2. now fill in the x and y with the x(t) and y(t)

= -2cos(t)sin(t) -2sin(t)cos(t)
3. simplify:

= -4cos(t)sin(t)

I hope this helps....