Differentiation of y=√x by First Principle.

First principle differentiation method uses the core idea of finding the slope of a function with respect to an independent variable.

The steps involved in differentiation by first principle includes:

Add a corresponding change to x and y (i.e ∆x to x and ∆y to y).
Subtract y from both, recalling that y =f(x).
Divide both sides of the mathematical statement in (2) above by ∆x.
Take the limit of the statement in (3) above as ∆x → 0.

Brief video tutorial reminder:

Now let's consider how to do the differentiation of y=√x using first principle method. This includes the use of binomial expansion of negative and rational index, if you don't have an idea of how to do this, simply watch our video on binomial expansion involving rational index

For the differentiation of y=√x using first principle method, see the attachment below: