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Mathematics
Mathematics
Problem
Consider the function
y
=
(
sin
(
2
x
2
+
1
)
)
5
y = \bigl(\sin(2x^{2}+1)\bigr)^{5}
y
=
(
sin
(
2
x
2
+
1
)
)
5
. (i) Find
d
y
d
x
\displaystyle \frac{dy}{dx}
d
x
d
y
and express your answer in simplified factored form. (ii) Hence evaluate
d
y
d
x
\displaystyle \frac{dy}{dx}
d
x
d
y
at
x
=
0
x = 0
x
=
0
. (iii) Verify that your simplified derivative from part (i) reduces correctly when
x
=
0
x=0
x
=
0
.
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