Tutorial02W_Ans.pdf - MAT133Y5Y Tutorial 01 - Winter 2020...

MAT133Y5Y
Tutorial 01 - Winter 2020
January 20 - 24, 2020
1. For each of the following functions, find a general formula for the n th derivative for any n ∈ N .
(a) f ( x ) = e
4 x
(b) g ( s ) = ln(1 - s )
(c) h ( z ) = ze
z
(d) ‘ ( w ) = w ln( w )
(e) p ( u ) = log
a
( u ) ( a > 1)
(f) m ( v ) = a
kv
, ( a > 1 , k ∈ R )
(g) r ( t ) = t
m
, ( m ∈ N )
2. By any means necessary to you, determine the derivatives of the following functions:
(a) f ( x ) = ( x - 1)( x - 2)
2
( x - 3)
3
( x - 4)
4
( x - 5)
5
(b) g ( s ) =
e
s
(
√
s + 3) ln( s )
s 4 ( s 2 + 2)
(c) h ( z ) =
√
z z + 1
(d) ‘ ( w ) = ( w
w
)
w
(e) p ( u ) = u
( u
u
)
(f) m ( v ) = α ( v )
α ( v )
+ β ( v )
β ( v )
, α, β differentiable and positive.
1

Answers: