Quantitative Methods
Lecture 6
Differential calculus
•BAKVM

Outline of the lecture
•The derivative of a function
•Derivatives of elementary functions

The derivative of a function
•Motivation: instantaneous velocity and the line tangent to the graph
of a function
•
•Rules to calculate the derivative
•
•Chain rule

The derivative of a function



The derivative of a function



The derivative of a function



The derivative of a function



The derivative of a function



The derivative of a function



The derivative of a function



The derivative of a function



Rules to calculate the derivative I



Rules to calculate the derivative II



Rules to calculate the derivative III



Chain rule



Examples:  Derivatives of elementary functions I



Examples:  Derivatives of elementary functions II



Examples:  Derivatives of elementary functions III



Examples:  Derivatives of elementary functions IV



Examples:  Derivatives of elementary functions IV



Examples:  Derivatives of elementary functions V



Examples:  Derivatives of elementary functions VI



Examples:  Derivatives of elementary functions VII



Examples:  Derivatives of elementary functions VIII



The rules of differentiation

•

•

•
•
•
•
•
•

1.
Let f(x) and g(x) be functions with the derivative
in the interval               Then:

Derivatives of elementary functions

•

•

•
•
•
•
•
•

1.

Examples

•

•

•
•
•
•
•
•

1.