Math Is Fun Forum

jubadedo

Member

Registered: 2015-04-05

Posts: 19

Simplifying this function for partial differentiation

Hi guys,
I'm studying for this upcoming test. In one of the examples when they find f(x,y) for the function

They differentiate with respect to x first and get

then they simplify it to

Can someone please explain how they reached this step? I'm utterly confused over how to simplify it to that form. I know the y in the numerator comes from the y in the original function, so I guess my question is how they simplified the denominator so elegantly. Thank you very much!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Simplifying this function for partial differentiation

hi jubadedo

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jubadedo

Member

Registered: 2015-04-05

Posts: 19

Re: Simplifying this function for partial differentiation

Thank you so much bob!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Simplifying this function for partial differentiation

Hi all,

Technically, that simplification is correct only if y is not negative. Otherwise, you'd need to have |y| instead of y in the numerator there.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.