Note that the exponent on the variable must be exactly 1. Also, note that (a) cannot be zero – if it were, we wouldn’t have a variable left!
In this section we define the derivative of a function at a point and as a function itself. paul's math notes
We’ll start solving equations by looking at the simplest type of equation: in one variable. Note that the exponent on the variable must be exactly 1
A linear equation in one variable is any equation that can be written in the form: [ ax + b = 0 ] where (a) and (b) are real numbers with (a \ne 0). We’ll start solving equations by looking at the
If the limit exists at a specific ( x = a ), we say ( f ) is at ( a ).
: [ f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a} ] Note from Paul : Always remember – the derivative is a limit , not just a formula. Learn the definition first, then the shortcuts. Most mistakes come from forgetting what the derivative actually means.
