differentiate x+1/x²-4
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Answer:
f
(
x
)
=
1
x
2
−
4
f(x)=1x2-4
Rewrite
1
x
2
−
4
1x2-4 as
(
x
2
−
4
)
−
1
(x2-4)-1.
d
d
x
[
(
x
2
−
4
)
−
1
]
ddx[(x2-4)-1]
Differentiate using the chain rule, which states that
d
d
x
[
f
(
g
(
x
)
)
]
ddx[f(g(x))] is
f
'
(
g
(
x
)
)
g
'
(
x
)
f′(g(x))g′(x) where
f
(
x
)
=
x
−
1
f(x)=x-1 and
g
(
x
)
=
x
2
−
4
g(x)=x2-4.
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−
(
x
2
−
4
)
−
2
d
d
x
[
x
2
−
4
]
-(x2-4)-2ddx[x2-4]
Differentiate.
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−
2
(
x
2
−
4
)
−
2
x
-2(x2-4)-2x
Rewrite the expression using the negative exponent rule
b
−
n
=
1
b
n
b-n=1bn.
−
2
1
(
x
2
−
4
)
2
x
-21(x2-4)2x
Combine terms.
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−
2
x
(
x
2
−
4
)
2
-2x(x2-4)2
f
(
x
)
=
1
Step-by-step explanation:
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