DERIVATIVE OF SQUARE ROOT OF X USING FIRST PRINCIPLE

Formula to find derivative of a function f(x) by first principle :

This is also called as limit definition of the derivative.

Derivative of x using first principle :

Let f(x) = x.

Solved Problems

Find the derivative of each of the following.

Problem 1 :

Solution :

We already know the derivative of √x, which is ¹⁄2. We can find the derivative of the given function using chain rule as shown below.

Problem 2 :

Solution :

Problem 3 :

Solution :

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :

Problem 7 :

Solution :

Problem 8 :

Solution :

Problem 9 :

Solution :

Problem 10 :

Solution :

Problem 11 :

Solution :

Problem 12 :

Solution :

Problem 13 :

Solution :

Problem 14 :

Solution :

Problem 15 :

Solution :

Problem 16 :

Solution :

Problem 17 :

Solution :

Problem 18 :

Solution :

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