Differentiation Cheat Sheet

Generic Algebraic Equations

Laws of Logarithms

Chapter 0: Precalculus
Terms involved in function
Inequality to solve

Domain
Range

Equation
Transformation

translation of units to the right

translation of units to the left

translation of units to vertically up

translation of units to vertically down

reflection in y-axis

reflection in x-axis

scaling along y-axis by factor

scaling along x-axis by factor
Chapter 1: Limits & Continuity
If, then

Squeeze Theorem
Suppose, if, then
If, then and
Chapter 2: Derivatives

Function
Derivative

Constant Rule

Constant Multiple Rule

Sum Rule

Product Rule

Quotient Rule

Chain Rule /
Composite

Implicit Differentiation

Inverse Functions

Parametric

Differentiate powers

Trigonometry Identities

Chapter 3: Applications of Derivatives I
Equation of straight line:
Equation of tangent line:
Distance of 2 points:
Parametric Equations:
Properties
Test
Increasing
on if
Decreasing
on if
1-1
If always increasing or always decreasing
Concave Upwards concave upwards on if Concave Downwards concave downwards on if Inflexion point
Point is point of inflexion if concavity changes at

Taylor series of at Maclaurin Series (special case of Taylor series when
Coefficient of or term

Approximation using Taylor Polynomials Stop at L’Hopital’s Rule

Chapter 4: Applications of Derivatives II
Abs MAX
Abs max at if
Abs MIN
Abs min at if
Local MAX
Local max at if in some
Local MIN
Local min at if in some
Critical Point

i) Not an end-point ii) Either iii) Or

First Derivative Test for Local Extrema
If changes from +ve to -ve at , then has local max at
If changes from -ve to +ve at , then has local min at If doesn’t change at , then has no local extremum at
First Derivative Test for Absolute Extrema
If AND , then has Abs MAX
If AND , then has Abs MIN
Second Derivative Test
If AND ,