I-Calculus
Derivative of Exponential function
Let
y
=
f
(
x
)
=
e
x
, then
d
y
d
x
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
=
lim
h
→
0
e
x
+
h
−
e
x
h
=
lim
h
→
0
e
x
e
h
−
e
x
h
=
lim
h
→
0
e
x
(
e
h
−
1
)
h
=
lim
h
→
0
e
x
(
e
h
−
1
)
h
=
(
e
x
)
lim
h
→
0
e
h
−
1
h
=
(
e
x
)
(
1
)
=
e
x
In the above, we have used the fact that
lim
h
→
0
e
h
−
1
h
=
1
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