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Mathematics
Mathematics
Problem
The function
f
(
x
)
=
x
3
+
2
x
2
−
cos
x
+
sin
x
f(x)=x^{3}+2x^{2}-\cos x+\sin x
f
(
x
)
=
x
3
+
2
x
2
−
cos
x
+
sin
x
is given. a. (i) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
. b. (ii) Show that
f
′
(
x
)
f'(x)
f
′
(
x
)
can be written as
x
(
3
x
+
4
)
+
(
sin
x
+
cos
x
)
x(3x+4)+\bigl(\sin x+\cos x\bigr)
x
(
3
x
+
4
)
+
(
sin
x
+
cos
x
)
.
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