Answer the following True or False:
Since
d
d
x
(
4
x
2
+
9
x
+
7
)
=
8
x
+
9
\displaystyle \frac{{d}}{{{\left.{d}{x}\right.}}}{\left({4}{x}^{{2}}+{9}{x}+{7}\right)}={8}{x}+{9}
d
x
d
(
4
x
2
+
9
x
+
7
)
=
8
x
+
9
and
d
d
x
sin
x
=
cos
x
\displaystyle \frac{{d}}{{{\left.{d}{x}\right.}}}{\sin{{x}}}={\cos{{x}}}
d
x
d
sin
x
=
cos
x
, the chain rule gives us:
d
d
x
sin
(
4
x
2
+
9
x
+
7
)
=
(
8
x
+
9
)
cos
x
\displaystyle \frac{{d}}{{{\left.{d}{x}\right.}}}{\sin{{\left({4}{x}^{{2}}+{9}{x}+{7}\right)}}}={\left({8}{x}+{9}\right)}{\cos{{x}}}
d
x
d
sin
(
4
x
2
+
9
x
+
7
)
=
(
8
x
+
9
)
cos
x
True
False
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