gradient and plane equations

Questions:
  1. What is [imath]z(x,y)[/imath]?
  2. Are you familiar with the Chain Rule?
  3. Can you compute [imath]\frac{\partial g}{\partial x}[/imath]? How about [imath]\frac{\partial g}{\partial y}[/imath]?
 
1642622484502.png
This is what i was able to get with those questions, but i’m not feeling great about gx and gy..
 
blamocur said:
Questions:
  1. What is [imath]z(x,y)[/imath]?
  2. Are you familiar with the Chain Rule?
  3. Can you compute [imath]\frac{\partial g}{\partial x}[/imath]? How about [imath]\frac{\partial g}{\partial y}[/imath]?
Click to expand...
I am also confused with what the function of f is, because just the gradient vector is given
 
zelda12 said:
I am also confused with what the function of f is, because just the gradient vector is given
Click to expand...
If you write down the chain rule for your problem you'll see that you don't really need to know what [imath]f[/imath] is, but knowing [imath]\frac{\partial f}{\partial x}, \frac{\partial f}{\partial z}, \frac{\partial f}{\partial z}[/imath] at the specified point is enough.
 
okay this is what i got!! but gx seems like an off number?? is my answer just this ordered pair?
1642622312135.png
 
Last edited by a moderator:
This does not look right. Can you write the formulas for
[math]\frac{\partial}{\partial x} \left(f(x, y, g(x,y))\right)[/math]and
[math]\frac{\partial}{\partial y} \left(f(x, y, g(x,y))\right)[/math]using the chain rule?
 
blamocur said:
This does not look right. Can you write the formulas for
[math]\frac{\partial}{\partial x} \left(f(x, y, g(x,y))\right)[/math]and
[math]\frac{\partial}{\partial y} \left(f(x, y, g(x,y))\right)[/math]using the chain rule?
Click to expand...
for the third coordinate is it g(x,y) or z(x,y)??
 
blamocur said:
This does not look right. Can you write the formulas for
[math]\frac{\partial}{\partial x} \left(f(x, y, g(x,y))\right)[/math]and
[math]\frac{\partial}{\partial y} \left(f(x, y, g(x,y))\right)[/math]using the chain rule?
Click to expand...
1642624599083.png
 
Last edited by a moderator:
This does not look like the chain rule. Can you write it for a more general case, i.e. [imath]\mathbb R^2 \Rightarrow \mathbb R^3 \Rightarrow \mathbb R^1[/imath], or [imath]f(p(x,y), q(x,y), r(x,y))[/imath] ?
 
blamocur said:
This does not look like the chain rule. Can you write it for a more general case, i.e. [imath]\mathbb R^2 \Rightarrow \mathbb R^3 \Rightarrow \mathbb R^1[/imath], or [imath]f(p(x,y), q(x,y), r(x,y))[/imath] ?
Click to expand...
Alternately, can you show the formula for the chain rule you have in your text book or lecture notes?
 
blamocur said:
Alternately, can you show the formula for the chain rule you have in your text book or lecture notes?
Click to expand...
chain rule.PNG
This is a thing I really struggle with, but I feel like once I get the staring equations, I can carry the rest out..
 
blamocur said:
This does not look like the chain rule. Can you write it for a more general case, i.e. [imath]\mathbb R^2 \Rightarrow \mathbb R^3 \Rightarrow \mathbb R^1[/imath], or [imath]f(p(x,y), q(x,y), r(x,y))[/imath] ?
Click to expand...
I might have attached a photo of the wrong work before..
 

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zelda12 said:
View attachment 30777
This is a thing I really struggle with, but I feel like once I get the staring equations, I can carry the rest out..
Click to expand...
This one is looks correct for single variables. Want to find the formula for multi-variable (see post #13)?

P.S. I like using [imath]F[/imath] for the composite function to avoid confusion with [imath]f[/imath].
 
blamocur said:
This one is looks correct for single variables. Want to find the formula for multi-variable (see post #13)?

P.S. I like using [imath]F[/imath] for the composite function to avoid confusion with [imath]f[/imath].
Click to expand...
post 13?
 
blamocur said:
This one is looks correct for single variables. Want to find the formula for multi-variable (see post #13)?

P.S. I like using [imath]F[/imath] for the composite function to avoid confusion with [imath]f[/imath].
Click to expand...
chain rule multi.PNG
okay i found this, but am not sure about application
 
blamocur said:
Sorry, I meant post 11, the one about the multi-variable version of the chain rule.

( I am not too bright today, am I? Should think about some excuse :))
Click to expand...
haha no worries... even looking at that I am still so lost

its just not clicking in my brain
 
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