find the derivative of the following x - 1/x
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Answered by
2
Answer:
Let f(x)=
x−1
x+1
Thus using first principle,
f
′
(x)=
h→0
lim
x
f(x+h)−f(x)
=
h→0
lim
h
(
x+h−1
x+h+1
−
x−1
x+1
)
=
h→0
lim
h
1
[
(x−1)(x+h−1)
(x−1)(x+h+1)−(x+1)(x+h−1)
]
=
h→0
lim
h
1
[
(x−1)(x+h−1)
(x
2
+hx+x−x−h−1)−(x
2
+hx−x+x+h−1)
]
=
h→0
lim
h
1
[
(x−1)(x+h−1)
−2h
]
=
h→0
lim
[
(x−1)(x+h−1)
−2
]
=
(x−1)(x−1)
−2
=
(x−1)
2
−2
Answered by
1
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