Differentiating $ x^{a}y^{b} = c $, in its simplest form. $$ x^{a}y^{b} = c,  $$
where a, b and c are constants. My attempts so far
$$ \frac{dy}{dx} = ax^{a - 1}by^{b - 1}$$
$$ \frac{d^2y}{dx^2} = (a^2 - a)x^{a-2}(b^2 - b)y^{b - 2} $$
I think that these first and second derivatives are correct, however my issue is, are these the derivatives in their simplest form?
Any hints or inputs are welcomed.

Assuming this is implicit then,
$$\frac{d}{dx}y^n=ny^{n-1}\frac{dy}{dx}$$
Use together with the product rule for correct solution
