{a}^{3} {(x - a)}^{- x} + 3a ^{2} (x - a) ^{1 - x} + (x - a) ^{3 - x}
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Answer:
Consider the given expression.
y=tan
−1
(
a
3
−3ax
2
3a
2
x−x
3
)
Let,
x=atanθ
θ=tan
−1
a
x
Therefore,
y=tan
−1
[
a
3
(1−3tan
2
θ)
a
3
(3tanθ−tan
3
θ)
]
y=tan
−1
(tan3θ)
y=3θ
y=3tan
−1
a
x
Differentiate y with respect to x.
dx
dy
=3×
1+(
a
x
)
2
1
×
a
1
dx
dy
=
a
2
+x
2
3a
Hence, this is the required result.
Step-by-step explanation:
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