Partial Differentiation of this Equation in x and y

  • #1
Martyn Arthur
84
16
Homework Statement
Trying to get to fxx
Relevant Equations
Please see screen print
Hi;
please see below I am trying to understand how to get to the 2 final functions. They should be the same but 6 for the first one and 2 for the second?
(I hope my writing is more clear than previously)
There is an additional question below.
thanks
martyn
1707919506461.png

I can't find a standard derivative for cos^2 theta?
 
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  • #2
Martyn Arthur said:
I can't find a standard derivative for cos^2 theta?

Use the chain rule.
 
  • #3
Please show your work and don’t simply post images of your result. Type out your work.
 
  • #4
Your two first partials are correct, but your notation isn't.
These aren't f(x) and f(y) as you wrote. They are ##f_x(x, y)## and ##f_y(x,y)## respectively. They can also be written more compactly as ##f_x## and ##f_y##.
Martyn Arthur said:
I can't find a standard derivative for cos^2 theta?
It might be helpful to think of this as ##(\cos(\theta))^2## and then use the chain rule, as @pasmith recommended.

Orodruin said:
Please show your work and don’t simply post images of your result. Type out your work.
I agree. In the lower left corner, click on the link that says "LaTeX Guide." A few minutes spent reading that will be very helpful.
 
  • #5
Martyn Arthur said:
Homework Statement: Trying to get to fxx
Relevant Equations: Please see screen print

Hi;
please see below I am trying to understand how to get to the 2 final functions. They should be the same but 6 for the first one and 2 for the second?
No. Why are you saying that?

If you can solve that ##f_x(x,y) = 6x-2y-10## then I'm sure that you can calculate ##f_{x,y}(x,y)##. It's simply the derivative of ##6x-2y-10## with respect to ##y##.
Do something similar for ##f_{y,x}##.
 

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