Fellas, I have just learned this formula for computing the total derivative of a function $f(x, y)$ with respect to $x$ from its partial derivatives as follows:
$\frac{d}{dx}f(x,y)=\frac{∂f}{∂x}+\frac{∂f}{∂y}\frac{dy}{dx}$
But I can't understand why this equality is true. I have looked for proofs of this, but they are very technical proofs, hard to understand. Can anyone explain to me the basic intuition behind it?