Partial Differentiation of this Equation in x and y

[Martyn Arthur]

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

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

 

[pasmith]

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

Use the chain rule.

 

[Orodruin]

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

 

[Mark44]

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 $f_y$.

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.

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.

 

[FactChecker]

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 $f_{y,x}$.