Partial derivatives

[JAY6150]

Can anyone please help me with question

 

[tkhunny]

Have you tried ANYTHING? You did not SHOW us anything.

What is d/dx h(y)

 

[Steven G]

Different textbook books/instructors define f_xy(x,y) so can you give us your definition along with your attempt?

 

[Steven G]

Can anyone please help me with question

View attachment 28756

Can you please supply us with your definition of help?

 

[Dr.Peterson]

Can anyone please help me with question

View attachment 28756

We can't be sure what sort of help you need, because you didn't tell us. But one thing you may be missing is that when they write h(y), they are telling you that there is no x in that term; as far as x is concerned, h(y) is a constant. For example, f(x,y) might be 2x² + 7y⁵, so that g(x) = 2x² and h(y) = 7y⁵. The first is a function only of x, and the second is a function only of y.

So what do you get when you find f_x(x,y)? Don't worry about the fact that you don't know what g(x) is; just call its derivative g'(x) and keep going. When you do the next step, differentiating a second time with respect to y, you'll see something useful happening.