DIFFERENTIATION

FIRST PRINCIPLES

Questions: 2001 6b(ii), 1999 I 6b, 1997 I 6b(i), 1996 I 7a, 1994 I 7a.

So far, the functions have been asked.
Addition Rule: 2002 I 6b(i)

Product Rule: 2000 I 6b(i), 1995 I 6c(ii).

POWER RULE

Note:

Learn: .

Questions: 2001 I 6b(i), 1998 I 7a, 1997 I 6a(i)

PRODUCT RULE

Questions: 2003 I 7c(ii), 2001 I 7b(ii), 1997 I 6a(ii), 1995 I 6b(i),

QUOTIENT RULE

Questions: 2004 I 6a, 2001 I 6a, 2000 I 6a(ii), 1996 I 6a(i), 1995 I 6a(ii), 1994 I 6a(i).

SIMPLE CHAIN RULE

EXAMPLE

Differentiate: (a) (b)

ANSWER

(a) Let then .

(b) Let

Questions: 2005 I 6a(i), 2003 I 6a, 2003 I 7a(i), 2002 I 6a, 2002 I 6b(ii), 2002 I 6c, 2000 I 6a(i),
1999 I 6a, 1999 I 7a, 1998 I 6a, 1997 I 6b(ii), 1996 I 6a(ii), 1996 I 6b(i), 1995 I 6a(i), 1995 I 6b(ii), 1994 I 6a(ii), 1994 I 7b(i).

TABLE FUNCTIONS

e.g.

Questions: 2005 I 6a(ii), 2004 I 7c, 2004 I 6b(i), 2003 I 7a(ii), 2002 I 7b(i), 2002 I 7c, 2001 I 7b(i), 2000 I 6b(ii), 1994 I 6b(i)

CHAIN RULE WITH PRODUCT, QUOTIENT OR CHAIN RULE

Questions: 2005 I 6b, 2003 I 7c(i), 1995 I 6b(i), 1995 I 7c

SLOPE OF THE TANGENT

If is a tangent to the curve at the point
then

Questions: 2003 I 6c(iii), 2000 I 6c(iii), 1996 I 7b,

PARAMETRIC EQUATIONS

Questions: 2005 I 7b(i), 2004 I 7b, 2003 I 7b(i), 2002 I 7b(ii), 2001 I 6c, 2000 I 7b, 1999 I 7b(i), 1998 I 7b,
1997 I 7b(ii), 1996 I 6c(i), 1994 I 7b(ii), 1994 I 7c.

IMPLICIT FUNCTIONS

EXAMPLE

ANSWER

Questions: 2005 I 7b(ii), 2003 I 7b(ii), 2002 I 7a, 2000 I 7a, 1999 I 7b(ii), 1997 I 6c, 1997 I 7b(i), 1996 I 7c, 1995 I 7a,

NEWTON-RAPHSON METHOD.

Questions: 2005 I 7c, 2003 I 6b, 2001 I 7a, 1998 I 7c, 1997 I 7a, 1996 I 6b(ii), 1995 I 7b,

ASYMPTOTES

Horizontal Asymptote:

Vertical Asymptote:
(This is usually because would result in division by zero.)

Questions: 2005 I 6c, 2000 I 6c(i), 1998 I 6c (first part), 1997 I 7c

TURNING POINTS AND POINTS OF INFLEXION.

A turning point is a solution to the equation

A turning point is a local maximum if .

It is a local minimum if .

A point of inflexion is a solution to the equation

Questions: 2003 I 6c(i), 2002 I 6c, 2001 I 7c, 2000 I 6c(ii), 2000 I 7c, 1999 I 6c,
1999 I 7c1998 I 6c (second and third part), 1996 I 6c(ii), 1995 I 6c(i), 1994 I 6b(ii),
1994 I 6c.

Rates of Change

If s(t) is the distance of a body from a certain point at a time t, then

2004 I 7a

Miscellaneous

Increasing function i.e. : 2003 I 6c(ii)

Differential Equations: 1998 I 6b

Max and min related to roots: 2004 I 6c