Let $f(x,y) = x^4y + 6xy^3 + 3x^4$.
(a) Find $f_x$.
(b) Find $f_y$.
I believe that I should make the equation equal to the function that I am looking for to solve the question. Would I be able to find the answer this way, and if not, how should I?
2026-04-12 16:59:14.1776013154
Finding $f_x$ and and $f_y$ in a $f(x,y)$ function.
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Let $f(x,y) = x^4y + 6xy^3 + 3x^4$.
(a) We find $f_x$ by holding all the other variables (other than $x$) as constants. In this setting, we are holding $y$ as a constant. So we obtain: $f_x = f_x (x,y)= 4x^3 y + 6y^3 +12 x^3$.
(b) Similarly, $f_y = f_y(x,y)=x^4 +18xy^2$.