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.
Let us differentiate f from first principles.
Therefore, we can define the gradient function as