Questions about the midterm exam?
Reminder: Your cheat sheet must be WRITTEN or TYPED
by you.
The exam will cover up through (and including) section 2.5
(the chain rule).
True-false questions on pages 138–139:
1. “If
f
is continuous at
a
, then
f
is differentiable at
a
.”
..?.
.
False!
(See the note on page 88.)
The converse is however
true.
2. “If
f
and
g
are differentiable, then (
d
/
dx
) [
f
(
x
)+
g
(
x
)] =
f
′
(
x
) +
g
′
(
x
).”
..?.
.
True!
3. “If
f
and
g
are differentiable, then (
d
/
dx
) [
f
(
x
)
g
(
x
)] =
f
′
(
x
)
g
′
(
x
).”
..?.
.
False!
(See the warning before the Product Rule on page
106.)
E.g. take
f
(
x
) =
g
(
x
) =
x
.

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*Sign up*4. “If
f
and
g
are differentiable, then (
d
/
dx
) [
f
(
g
(
x
))] =
f
′
(
g
(
x
))
g
′
(
x
).”
..?.
.
True!
But someone might think that
(
d
/
dx
) [
f
(
g
(
x
))] =
f
′
(
g
′
(
x
)), e.g., (
d
/
dx
) sin
x
2
= cos 2
x
.
Or they might think that
(
d
/
dx
) [
f
(
g
(
x
))] =
f
′
(
x
)
g
′
(
x
), e.g., (
d
/
dx
) sin
x
2
= (cos
x
) 2
x
.
5. “If

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