1. Partial Derivative

1. f(x,y)= x^2 / y, need fx and fy!

2.f(x,y)= x sin(xy), need fx and fy!

2. Originally Posted by littlesohi

1. f(x,y)= x^2 / y, need fx and fy!

2.f(x,y)= x sin(xy), need fx and fy!
to find fx, pretend y is a constant and differentiate as usual. to find fy, pretend x is a constant and differentiate as usual. where can you get with that?

3. so for the first one, I think fx = 2x but for fy I get confused can you help me please! I know the rules butusing the product or quotient rule confuses me.

4. Originally Posted by littlesohi
so for the first one, I think fx = 2x but for fy I get confused can you help me please! I know the rules butusing the product or quotient rule confuses me.
how is fx = 2x?

if you wanted to differentiate x^2 / 3 what would that be?

5. its over y! and for fx y is a constant no?

6. Yes, that is true. And to differentiate $x^2/y$ with respect to y, think of it as $A/y= Ay^{-1}$. What is the derivative of that?

7. Originally Posted by littlesohi
its over y! and for fx y is a constant no?
my point is, the constant stays! if you have a constant multiplying a variable, then the constant does not disappear when you differentiate. it stays there and multiplies the variable. this is a rule of differentiation you should be familiar with. $\frac d{dx} [cf(x)] = c \frac d{dx}f(x)$