# What did Newton contribute to the development of calculus?

Oct 9, 2014

Sir Isaac Newton was already well known for his theories of gravitation, and the motion of planets. His developments in calculus were to find a way to unify mathematics and the physics of planetary movement and gravity. He also introduced the notion of the product rule, the chain rule, Taylor series, and derivatives higher than the first derivative.

Newton mainly worked with function notation, such as:

• $f \left(x\right)$ to denote a function
• $f ' \left(x\right)$ to denote the derivative of a function
• $F \left(x\right)$ to denote an antiderivative of a function

So, for example, the product rule looks like this:
$\text{Let } h \left(x\right) = f \left(x\right) g \left(x\right) .$
$\text{Then } h ' \left(x\right) = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

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