Differentiability
“If the point of a function IS differentiable, then it MUST BE continuous at the point.”
Example of NOT differentiable points:
differentiable
Chain Rule
One of the core principles in Calculus is the Chain Rule.
Refer to Khan academy article: Chain rule▶ Proceed to Integral rule of composite functions: U-substitution
▶ Proceed to Integral rule of composite functions: U-substitution
Derivatives of Trig functions
Implicit differentiation
Bit hard to understand it in the first place.
What is Implicit & Explicit
Related Rates
Just so you know, related rates is actually the Application of Implicit Differentiation by using Chain Rule in the form of dy/dx = dy/du * du/dx.
related rates
Implicit Differentiation
dy/dx = dy/du * du/dx
f'(x)
dy/dx
f''(x)
d²y/dx²
Second derivatives
Derivative of Inverse functions
IT’S DERIVED FROM THE CHAIN RULE:
CHAIN RULE
Derivative of Inverse Trig
Derivative of exponential functions
It’s save a lot of time of life not to dig in how mathematicians developed these formulas.If you do want to, refer to Khan’s lecture: Exponential functions differentiation intro
Existence Theorems
Existence theorems includes 3 theorems: Intermediate Value Theorem, Extreme Value Theorem, Mean Value Theorem.
Intermediate Value Theorem
Extreme Value Theorem
Mean Value Theorem
Refer to Khan academy: Existence theorems intro
L'Hopital's Rule
LHopital's Rule helps us to find the limit of an Undefined limits, like 0/0, ∞/∞ and such.It's quite simple to apply and very convenient to solve some problems.
L
Undefined
0/0
∞/∞
Refer to L'Hôpital's rule
L'Hôpital's rule
▶ Back previous note on: Asymptote…
▶ Back previous note on: Asymptote
