Page 302 - DMTH201_Basic Mathematics-1

Unit 11: Parametric Differentiation

Notes
dy
Example: Find , if, x , t y 1/ t
dx
Solution:
dx 1 dy 1
Differentiating w.r.t. t, we get , 3/2
dt 2 t dt 2t
1
dy dy /dt 2t 3/2 1
dx dx /dt 1 t
2 t

dy
t
e
Example: Find , if, x 2 ,y 3e t
dx
Solution:
dx t dy t
2 , 3e
e
dt dt
dy dy /dt
dx dx /dt

3e t
2e 2t

3
2e 2t

dy
Example: Find , if, x e t log ,y e t log t
t
dx
Solution:
dx t 1 t
e logt e
dt t

1
t
e log t
t
dy 1
e t log t e t
dt t
1
e t log t
t
dy e t 1 log t
dy dt t
dx dx e t 1 log t
dt t

1 t logt
e 2t 1 t log t

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