Holding the other parts constant
It seems like ages ago – but it was only yesterday – that I wrote about differentiating functions with the variable in both the base and the power. Back there, I had learned that the derivative of a function like f(x)g(x) is the sum of the derivative when you pretend f(x) is constant and the derivative when you pretend g(x) is constant.
Since then I have realised that this idea actually dictates ALL of the differentiation rules where two functions are combined through an arithmetic operation! It’s everywhere!
The titles of the two blog posts in the series are:
- Differentiating exponentials: two wrongs make a right
- Holding the other parts constant: it's everywhere!