It is a powerpoint presentation that discusses about the lesson or topic of Derivatives and Differentiation Rules. It also encompasses some formulas, definitions and examples regarding the said topic.

1. Derivatives
Basic Calculus 11

2. Derivatives
It is the measure of the sensitivity of the
change of the function value with respect to a
change in its input value.

3. Differentiation
It is the action or process of computing a
derivative of a function.

4. Derivatives
The derivative f(x) with respect to 𝑓′
(x) is defined
as:

5. Example:

6. Example:
f(x) =
𝑥2+1
5𝑥−3
Rewrite the two equations as:
A = 𝑥2
+ 1
B = 5x - 3

7. Example:
By using the quotient rule:
𝑓′
𝑥 =
2𝑥 5𝑥 − 3 − 𝑥2
+ 1 5
(5𝑥 − 3)2
Expand and Group to obtain f’ (x):
𝑓′
𝑥 =
5𝑥2
− 6𝑥 − 5
(5𝑥 − 3)2

8. Continuity and
Differentiability
If y = f(x) is differentiable at a, then f must
also be continuous at a.
Any differentiable function must be
continuous at every point in its domain.

9. Rules in
Differentation

10. Differentiation
It is a process of finding a function
that outputs the rate of change of one
variable with respect to another
variable.

13. Inverse Function Rule

14. Reciprocal Rule
𝟏
𝒗
’ =−
𝒗 𝟐
𝟐