MATH011101
MATH011101
This question paper consists of 5 printed
pages, each of which is identied by the
reference MATH011101
Only approved basic scientic
calculators may be used.
c UNIVERSITY OF LEEDS
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 5 Functions and Dierentiation
These examples count towards the assessment of the module and should be
handed in on Monday 11th N
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 6 Further Dierentiation, Chain Rule
These examples count towards the assessment of the module and should be
handed in on Monday
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 6
In many questions we shall use the chain rule (function of a function),
dy
dy du
=
. Then rewrite anything involving u in ter
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 5
If we dierentiate xp we obtain p.xp1 , and if we dierentiate axp we get
a.p.xp1 (when a and p are numbers).
1. 6x61 = 6x5 .
2
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 4 Trigonometric Functions
These examples count towards the assessment of the module and should be
handed in on Monday 4th Novemb
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 2 Indices
These examples count towards the assessment of the module and should be
handed in on Wednesday 23rd October. Do not us
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 3 Coordinate Geometry
These examples count towards the assessment of the module and should be
handed in on Monday 28th October.
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 3
1. The idea is to express every equation in the form y = mx + c; then the
gradient is m and the intercept c. So we solve each
MATH011101
MATH011101
This question paper consists of 3 printed
pages, each of which is identied by the
reference MATH011101
All calculators must carry an approval
sticker issued by the School of
Math
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 2
We repeatedly use the rules: a0 = 1, a1 = a, ap+q = ap aq , ap /aq = apq ,
(a ) = apq , and the pth root of a is a1/p . Some
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 1 Basic Algebra
These examples count towards the assessment of the module and should be
handed in on Monday 14th October. Do not