Method to solve

Step 1.Try to simplify the equation in such a way that it resemble the first principle of derivative.

Step 2.Find the value of f(x)

Step 3.Find f'(x) using first principle.

Step 4.Find the value of x such that on substituting it resembles the question

Let’s understand it better using an example problem.

The dictionary meaning of “disguise” is “unrecognizable”. Disguised derivative means “unrecognized derivative”. In this type of problems, the definition of derivative is hidden in the form of limit. At a glance, the problem seems to be solvable using limit properties but it is much easier to solve it using the first principle of derivative. So, this type of problems are known as derivative in disguise.

Before proceeding further, we need to revise the first principle of derivative. Finding the derivative of a function by computing this limit is known as differentiation from first principles. Derivative by first principle refers to using algebra to find a general expression for the slope of a curve. It is also known as the delta method. The derivative is a measure of the instantaneous rate of change, which is equal to