Partial Differentiation of this Equation in x and y

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

I can't find a standard derivative for cos^2 theta?

Martyn Arthur said:

I can't find a standard derivative for cos^2 theta?

Use the chain rule.

Please show your work and don’t simply post images of your result. Type out your work.

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.

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}##.