I-Calculus
Derivative of the natural logarithmic function
We know that
y
=
e
x
and
x
=
ln
y
are inverse functions of each other.
Also, we know that
d
y
d
x
=
e
x
.
So
d
x
d
y
=
1
d
y
d
x
=
1
e
x
=
1
y
Usually we write any function as a function of
x
, so, if we write
y
=
ln
x
, then
d
y
d
x
=
1
x
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