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Derivative of an exponential function
Derivative of an Exponential Function.
Example-10:
(i)
x
ey =
Solution:
x
e
dx
dy
=
(ii)
x
ey 3
=
Solution:
( )3 3
3x xdy d
e e
dx dx
= =
(iii) ( )24
+= xey x
Solution:
( ) ( ) xx
e
dx
d
xx
dx
d
e
dx
dy 44
22 +++=
( ) ( ) ( )x
dx
d
exe xx
421 44
++=
( ) ( )42 44 xx
exe ++=
( )? ?4214
++= xe x
( )8414
++= xe x
( )944
+= xe x

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  • 2. Derivative of an Exponential Function. Example-10: (i) x ey = Solution: x e dx dy = (ii) x ey 3 = Solution: ( )3 3 3x xdy d e e dx dx = = (iii) ( )24 += xey x Solution: ( ) ( ) xx e dx d xx dx d e dx dy 44 22 +++= ( ) ( ) ( )x dx d exe xx 421 44 ++= ( ) ( )42 44 xx exe ++= ( )? ?4214 ++= xe x ( )8414 ++= xe x ( )944 += xe x