0
$\begingroup$

Define $F$ as $$F(x,y,u,v) = x^3e^{uv} + vy^2\sin{\left(y^3\right)}$$ where $u(x,y) = x^2y$ and $v(x,y) = xy^3$.

Define $f(x,y) = F(x,y,u(x,y),v(x,y)$.

Determine $\dfrac{\partial F}{\partial x}$ and $\dfrac{\partial f}{\partial x}$.

How to do this for $F$ and $f$ respectively? Aren't $F$ and $f$ the same? I'm confused. Thanks

  • 1
    What you are looking for is the *multivariable chain rule*.2012-11-06
  • 0
    chain rule tutorials doesn't have this situation.2012-11-07
  • 0
    What you have is $f$ is a "function" of $F$ I.e. $f(F)=F$.2012-11-07

1 Answers 1