Leibniz' Rule

Leibniz' rule allows us to "move" the differentiation operator into the integral expression; this appears to permit us to apply differentiation and integration in either order if both appear in an equation.

A simple example is

$$\frac{d}{dx} \int{y(x) \ dx} = \int{ \frac{dy}{dx} \ dx}$$

In this example we see that we can rewrite the integral equation; further shorthand allows us to "cancel" dx and evaluate the integral analytically to get an expression of just y.

Formal Definition

We can make this more rigorous so we don't need to additional shorthand of "canceling" dx. TODO