Question

What does it mean to take Derivative in Respect to x and Derivative in Respect to y. I get confuse on those terms.

Answer 1

for example, f(x,y)= 3x + 4y
Derivative respect to x, mean x now is variable and y become constant
fx= 3 + 0 = 3
Derivative respect to y, means y now is variable and x becomes constant
fy= 0 + 4= 4

Answer 2

If you have a function that has both x's and y's, for example \[f(x,y)=x^2+3xy^2\] then you can take derivatives "with respect to" x or y. If you take the derivative with respect to x, this means that you treat y as you would treat just any constant. So here, \[\frac{d}{dx}(x^2 + 3xy^2) = 2x + 3y^2\] Similarly, the derivative with respect to y treats x like a constant, giving \[\frac{d}{dy}(x^2 + 3xy^2) = 6xy\]
I hope this helps!

Answer 3

thank you very much both explaination helped me.