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 ,
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 ,