I am learning about differentiation (calculus) to work out derivatives at the moment. The maths I am learning is all about various different things in the economy, business and personal finance.

 

I previously wrote about compound interest in the post:  First order linear recurrence and compound interest from the book ‘Mathematics for Economics and Finance’ by Martin Anthony and Norman Biggs.

 

I am not learning about derivatives, the number e and logarithms.

 

I find it quite amazing how the trick of differentiation works where if you have 2x2 and find the derivative it becomes 4x. By multiplying the first number by the power and then reducing the power by one results in the derivative.

 

What are the chances of that? We live in a strange world.

 

The derivative is the change in the function at a given point. You might imagine the different between two points on a curve. The average rate of change of the curve is the gradient of a straight line between the two points. As the two points get closer together the gradient becomes nearer the rate of change at a single point. Calculus allows us to work out what the rate of change is at that single point.

 

Reference:

 

Wikipedia: Calculus (in particular look at the heading Differential calculus)