Page 303 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2
dy 3at 3at
Example: Find , if, x 3 y 3
dx 1 t 1 t
Solution:

dx 1 t 3 3a 3at 3t 2
dt 1 t 3 2

a
3 1 t 3 3t 3
1 t 3 2

3 1 2t 3
a
2
1 t 3
3at 2
y 3
1 t
dy 1 t 3 6at 3at 2 3t 2
dt 1 t 3 2

3at 2 t 3
3 (2 t 3 ) 2
at
3 2
)
(1 t 1 t 3
dy
dy dt 3at 2 t 3
dx dx 3 1 2t 3
a
dt
dy t 2 t 3
dx 1 2t 3

dy
Example: Find , if, x log t l 2 1 ,y t 2 1
dx
Solution:

dx 1 1
1 2t
dt t t 2 1 2 t 2 1

t 2 1 t
1 1
t t 2 1 t 2 1 t 2 1

dy 1 t
2t
dt 2 t 2 1 t 2 1

dy t
dy dt t 2 1 t
dx dx 1
dt t 2 1

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