Page 313 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes n 1 n
n n 1 ax bx n n 1 y
x 2 y n (n ) 1 y 0
2
2
d y
Example: Find 2 , if, x at 2 ,2y 2at
dx
Solution:
dx dy
2 , 2a
at
dt dt
dy
dy dt 2a 1
dx dx 2at t
dt

2
d y d 1 d 1 dt
dx 2 dx t dt t dx
1 1 dx
 2at
t 2 2at dt
1
2at 3

2
d y c
,
Example: Find , if, x ct y
dn 2 t
Solution:
dy dx c
, c
dt dt t 2
c
dy dy /dt t 2 1
dx dx /dt c t 2
2
d y d 1
dx 2 dx t 2

d 1 dt 2 1 2
dt t 2 dx t 3 c ct 3

2
d y
Example: Find 2 , if, x 2 xy y 2 a 2
dx
Solution:
2
Differentiate x 2 xy y 2 a w.r.t. x
dy dy
2x x y 2y 0
dx dx
dy dy 2x y
x 2y 2x y ,
dx dx x 2y

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