When to use implicit differentiation?

Question

When a problem is expressed like this $F(x,y)$ then you are asked to find $F_x(x,y)$

My understand is that means you need to find the partial derivative of $x$, which means $y$ is held and treated as constant ? Is this correct or does it need to use that funny little partial derivative symbol ?

Thanks,

Answer 1

Your opinion is correct: $F_x$ means the derivative of $F$ with respect to the $x$ variable, and $y$ is kept constant. It is just an alternative notation to $$ \frac{\partial F}{\partial x}, \quad D_xF, \quad \partial_x F, \quad \partial_1 F. $$

Answer 2

$F_x(x,y)$, $F_y(x,y)$, and even just $F_x$ or $F_y$ are all notations for a partial derivative with respect to the subscript.

Answer 3

You we describing "partial differentiation", not "implicit differentiation". The symbols $$F_x(x,y)$$ and $$\frac{\partial F}{\partial x}(x,y)$$ mean the same thing.