# What did Leibniz contribute to the development of calculus?

Oct 9, 2014

Gottfried Wilhelm Leibniz was a mathematician and philosopher. Many of his contributions to the world of mathematics were in the form of philosophy and logic, but he is much more well known for discovering the unity between an integral and the area of a graph. He was primarily focused on bringing calculus into one system and inventing notation that would unambiguously define calculus. He also discovered notions such as higher derivatives, and analysed the product and chain rules in depth.

Leibniz mainly worked with his own invented notation, such as:

• $y = x$ to denote a function, in this case, f(x) is the same as y
• $\frac{\mathrm{dy}}{\mathrm{dx}}$ to denote the derivative of a function
• $\int y \mathrm{dx}$ to denote an antiderivative of a function

So, for example, the product rule looks like this:
$\text{Let } y = u v ,$ where u and v are both functions
$\text{Then } \frac{\mathrm{dy}}{\mathrm{dx}} = u \frac{\mathrm{dv}}{\mathrm{dx}} + v \frac{\mathrm{du}}{\mathrm{dx}}$

This notation can be overwhelming for some people, which is where Newton comes into the picture.