## 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

**3.2 THE EXPONENTIAL FUNCTIONS**

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

**3.4 THE CHAIN RULE**

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

**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

**3.7 IMPLICIT FUNCTIONS**

Implicit Functions