# Tag Archives for **calculus**

## Proof of separation of variables

Let’s say we have a differential equation: $$f(y) \dod{y}{x} = g(x)$$ Separation of variables says that we can simply “split” the derivative $\dod{y}{x}$ and write $$f(y) \dif{y} = g(x) \dif{x}$$ Then, we can integrate both sides: $$\begin{gather*} \int f(y) \dif{y} … Continue reading

## Quotient rule with determinants?

I’ve always found the quotient rule for differentiation hard to remember: $$\dod{}{x}\frac{f}{g} = \frac{f’g – g’f}{g^2}$$ I was looking on the Wikipedia page for the finite difference operator and noticed that they use the determinant in describing the quotient rule for … Continue reading