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.

Hint:
$$\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)$$
Then differentiate the $\frac{d}{dx}$ similarly.
Assuming you are not dealing with implicit differentiation otherwise you may need The Chain Rule as well as The Product Rule.
