VCE Mathematical Methods/Differentiation from First Principles

Theory Formula Given a function f, the rule of the derivative (sometimes called the "gradient") function is defined as . Method Remember that in order to evaluate a limit, we usually substitute the value given into the expression. However, with the above formula, substituting will result in a division by zero, which is mathematically impossible. Therefore,in order to make use of this formula, you need to substitute the rules and , then simplify to eliminate the fraction, and only then substitute . This is called differentiation from first principles. For example: Let Let us differentiate f from first principles. . Therefore, we can define the gradient function as Exercises Question One Differentiate the following functions from first principles. (a) (b) (c) (d) Question Two Differentiate the following functions from first principles. (a) (b) (c) (d)