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Mathematics
Mathematics
Problem
For
y
=
ln
(
sin
(
5
x
2
+
4
x
+
1
)
)
y=\ln\bigl(\sin\bigl(\sqrt{5x^{2}+4x+1}\bigr)\bigr)
y
=
ln
(
sin
(
5
x
2
+
4
x
+
1
)
)
, answer the following. a. (i) Find
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
, simplifying your result as far as possible. b. (ii) Hence calculate
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at
x
=
0
x=0
x
=
0
. (Leave your answer in exact form.)
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