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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
(
3
x
2
+
2
x
+
1
)
5
f(x)=\bigl(3x^{2}+2x+1\bigr)^{5}
f
(
x
)
=
(
3
x
2
+
2
x
+
1
)
5
. a. (a) State the formula for the derivative of a composite function
y
=
f
(
g
(
x
)
)
y=f\bigl(g(x)\bigr)
y
=
f
(
g
(
x
)
)
. b. (b) Obtain
f
′
(
x
)
f'(x)
f
′
(
x
)
in simplified form without expanding the binomial. c. (c) Hence, calculate
f
′
(
0
)
f'(0)
f
′
(
0
)
, giving the exact value.
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