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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
(
x
2
+
1
)
3
x
e
x
2
f(x)=(x^2+1)^{3x}\,e^{x^2}
f
(
x
)
=
(
x
2
+
1
)
3
x
e
x
2
for all real
x
x
x
. (a) Derive an explicit expression for
f
′
(
x
)
f'(x)
f
′
(
x
)
. All steps leading to the final simplified result must be shown. (b) Evaluate
f
′
(
0
)
f'(0)
f
′
(
0
)
. Show your numerical substitutions clearly.
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