CONTENT
- Meaning of differentiation/derived function.
- Differentiation from the first principle.
- Standard derivatives of some basic functions.
MEANING OF DIFFERENTIATION/DERIVED FUNCTION
The process of finding the differential coefficient of a function is called differentiation. Differentiation deals with the measure of the rate of change in a particular function when some quantities in the function is either increased or decreased. For example, given the function \(y = f(x) \), a change in \( x\) will produce a corresponding change in \(y\). When \(y\) is increased, \(x\) is bound to increase in proportion and vice versa. Note: The reverse of differentiation is integration.
DIFFERENTIATION FROM THE FIRST PRINCIPLE
The method of finding the derivative of a function from definition is called differentiation from the first principle. Note: A change in \(x\) to \(x + Δx \) produces a corresponding change in \(y \) to \(y + Δy \).
Example 1:
Differentiate the following from the first principle
(a) \(y = 2x + 5\)
(b) \(y = x^2 \)
SOLUTION
(a) \(y = 2x + 5\)
Take increment in both \(x\) and \(y\).
- NEW: Download the entire term's content in MS Word document format (1-year plan only)
- The complete lesson note and evaluation questions for this topic
- The complete lessons for the subject and class (First Term, Second Term & Third Term)
- Media-rich, interactive and gamified content
- End-of-lesson objective questions with detailed explanations to force mastery of content
- Simulated termly preparatory examination questions
- Discussion boards on all lessons and subjects
- Guaranteed learning