# Thread: Leibnitz notation: treating it as a quotient

1. ## Leibnitz notation: treating it as a quotient

Hi,

How is it that you're allowed to treat the derivative dy/dx as an actual quotient, f.ex. when calculating in integral by substitution such as: integral f(x) dx, if you the y=f(x), and dy/dx = g(x), so that dx = dy/g(x) and so integral f(x) dx = integral y/g(x) dy.

Clearly, we multiplied both sides of dy/dx = g(x) with dx! How is this possible? Isn't dy/dx just a notation denoting the derivative, not actual.... numbers?

/Yair

2. ## Re: Leibnitz notation: treating it as a quotient

Originally Posted by Yair1978
Hi,

How is it that you're allowed to treat the derivative dy/dx as an actual quotient, f.ex. when calculating in integral by substitution such as: integral f(x) dx, if you the y=f(x), and dy/dx = g(x), so that dx = dy/g(x) and so integral f(x) dx = integral y/g(x) dy.

Clearly, we multiplied both sides of dy/dx = g(x) with dx! How is this possible? Isn't dy/dx just a notation denoting the derivative, not actual.... numbers?

/Yair
This will make an order in your thoughts: Differential of a function - Wikipedia, the free encyclopedia

3. ## Re: Leibnitz notation: treating it as a quotient

In fact, once you have defined "differentials", the fact that $\frac{dy}{dx}= f(x)$ implies $dy= f(x)dx$ is important in integration.