MAT135 Unit 4: Calculating Derivatives
3.1 POWERS AND POLYNOMIALS
Derivative of a Constant Times a Function
Derivatives of Sums and Differences
Powers of x
Derivatives of Polynomials
The Tangent Line Approximation for Power Functions
Derivative of a Constant Times a Function
Derivatives of Sums and Differences
Powers of x
Derivatives of Polynomials
The Tangent Line Approximation for Power Functions
3.2 THE EXPONENTIAL FUNCTIONS
Derivatives of Exponential Functions and e
A Formula for the Derivative of a^x
Derivatives of Exponential Functions and e
A Formula for the Derivative of a^x
3.3 THE PRODUCT AND QUOTIENT RULES
The Product Rule
The Quotient Rule
The Product Rule
The Quotient Rule
3.4 THE CHAIN RULE
Intuition Behind the Chain Rule
The Derivative of a Composition of Function
Intuition Behind the Chain Rule
The Derivative of a Composition of Function
3.5 THE TRIGONOMETRIC FUNCTIONS
Derivatives of the Sine and Cosine
Derivative of the Tangent Function
Informal Justification of d (sin x) = cos x / dx
Derivatives of the Sine and Cosine
Derivative of the Tangent Function
Informal Justification of d (sin x) = cos x / dx
3.6 THE CHAIN RULE AND INVERSE FUNCTIONS
Derivative of ln x
Derivative of a^x
Derivatives of Inverse Trigonometric Functions
Derivative of a General Inverse Function
Derivative of ln x
Derivative of a^x
Derivatives of Inverse Trigonometric Functions
Derivative of a General Inverse Function
3.7 IMPLICIT FUNCTIONS
Implicit Functions
Implicit Functions