LORMA COLLEGES
Basic Education Schools
Senior High School
MOST ESSENTIAL LEARNING COMPETENCY
The learner applies the definition of the derivative of a function at a given number.
STEM_BC11DIIIe-2
The learner derives the differentiation rules
STEM_BC11D-IIIf-2
The learner applies the differentiation rules in computing the derivative of an
algebraic, exponential, logarithmic, trigonometric functions and inverse trigonometric
functions
STEM_BC11D-IIIf3
CONTENT STANDARDS
The learner demonstrates understanding of basic concepts of derivatives.
PERFORMANCE STANDARDS
The learner is able to formulate and solve accurately situational problems involving
extreme values.
Lesson 1 The Derivative of a Function
In mathematics, the derivative of a function of a real variable
measures the sensitivity to change of the function value with
respect to a change in its argument. Derivatives are a
fundamental tool of calculus.
DERIVATIVE is the change in a certain
function or an instant rate of change.
So, every derivative of 𝑓(𝑥) is a new
function 𝑓′(𝑥).
Based on the definition of derivative,
we can have the formula:
𝒇(𝒙 + ∆𝒙) − 𝒇(𝒙)
𝐟 ′(𝐱) = 𝐥𝐢𝐦
∆𝒙→𝟎 ∆𝒙
TAKE NOTE
Basic Education Schools
Senior High School
MOST ESSENTIAL LEARNING COMPETENCY
The learner applies the definition of the derivative of a function at a given number.
STEM_BC11DIIIe-2
The learner derives the differentiation rules
STEM_BC11D-IIIf-2
The learner applies the differentiation rules in computing the derivative of an
algebraic, exponential, logarithmic, trigonometric functions and inverse trigonometric
functions
STEM_BC11D-IIIf3
CONTENT STANDARDS
The learner demonstrates understanding of basic concepts of derivatives.
PERFORMANCE STANDARDS
The learner is able to formulate and solve accurately situational problems involving
extreme values.
Lesson 1 The Derivative of a Function
In mathematics, the derivative of a function of a real variable
measures the sensitivity to change of the function value with
respect to a change in its argument. Derivatives are a
fundamental tool of calculus.
DERIVATIVE is the change in a certain
function or an instant rate of change.
So, every derivative of 𝑓(𝑥) is a new
function 𝑓′(𝑥).
Based on the definition of derivative,
we can have the formula:
𝒇(𝒙 + ∆𝒙) − 𝒇(𝒙)
𝐟 ′(𝐱) = 𝐥𝐢𝐦
∆𝒙→𝟎 ∆𝒙
TAKE NOTE
