Differentiation using First Principles

“Hi my name is Jason, I am in Mr T’s Math Methods class, Today we learnt about differentation using first principles, it is an equation that allows us to figure out the derivative, which is the gradient, we use this so we can find out the instantaneous rate of change. It is kind of hard but once you learn it it gets easier. I have made a few mistakes but i can do it easier now that i have had some practice”.

Well, when I asked Jason to add a comment to my blog I must admit I was a bit nervous. But teaching is a risk taking business. I am impressed with Jason’s use of mathematical language – use of the words gradient and instantaneous rate of change in correct context, means he has taken in some of my teaching. Also I did not have to correct any of his spelling. Here is Jason’s setting out:

mm 005s

My class is starting to master this topic but some common mistakes today were:

1. Incorrect substitution of  (x+h) 

2. Confused between notations eg. y= and f(x), dy/dx and f ‘ (x)

3. Subtracting  f(x) incorrectly


The chocolate princess had trouble concentrating today without her usual supply of dark chocky, as well as thinking about her birthday tomorrow! She also got pooed on by a pink elephant!


About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
This entry was posted in Pedagogy and tagged , , , . Bookmark the permalink.

2 Responses to Differentiation using First Principles

  1. onias chikomo says:

    Thats understandable example of differentiate with first principle

  2. Can anybody help me find out Differentiation using First Principles of: y=(2x+3)^3/2

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