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Mathematics
Mathematics
Problem
Define
h
(
x
)
=
(
x
2
+
1
)
cos
x
x
+
(
3
x
−
2
)
sin
x
x
2
.
h(x)=\frac{(x^{2}+1)\cos x}{x}+\frac{(3x-2)\sin x}{x^{2}}.
h
(
x
)
=
x
(
x
2
+
1
)
cos
x
+
x
2
(
3
x
−
2
)
sin
x
.
(i) Differentiate
h
(
x
)
h(x)
h
(
x
)
with respect to
x
x
x
. (ii) Show that your result can be arranged in the form
h
′
(
x
)
=
(
1
+
3
x
−
3
x
2
)
cos
x
+
(
−
x
−
1
x
−
3
x
2
+
4
x
3
)
sin
x
.
h'(x)=\left(1+\frac{3}{x}-\frac{3}{x^{2}}\right)\cos x+\left(-x-\frac{1}{x}-\frac{3}{x^{2}}+\frac{4}{x^{3}}\right)\sin x.
h
′
(
x
)
=
(
1
+
x
3
−
x
2
3
)
cos
x
+
(
−
x
−
x
1
−
x
2
3
+
x
3
4
)
sin
x
.
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