Computing Derivatives True or False
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1.
Let
h
(
x
) =
e
3
x
+ 7
. Which is the best choice for the inside function?
->
g
(
x
) =
e
x
.
True
False
2.
The function
h
(
x
) is composed of two functions. The outside function is cos (□) and the inside function is ln
x
. Which formula best describes
h
? ->
h
(
x
) = cos
x
· ln
x
True
False
3.
The chain rule says that if
h
(
x
) =
f
(
g
(
x
)), then ->
h '
(
x
) =
f
(
g '
(
x
))·
f '
(
x
)
True
False
4.
Find the derivative of the function
f
(
x
) = (cos
x
)
-3
.
->
f '
(
x
) = 3(cos
x
)
-4
· sin
x
True
False
5.
Suppose
f
and
g
are inverses so that
f
(
g
(
x
)) =
x
. Then
->
True
False
6.
If
s
= 4
t
2
+ 3 and
r
= cos
s
, then to find the derivative of
r
with respect to
t
we would use the version of the chain rule that says ->
True
False
7.
The derivative of ln(5
x
6
+ 7
x
2
) is
->
True
False
8.
Which function's derivative is -7sin(
x
)cos
6
x
?
->
cos
7
x
True
False
9.
Find
y'
given that
y
is a function of
x
and
xy
+
x
+
y
= 0
->
True
False
10.
To use implicit differentiation on the equation
we need to use -> the chain rule but not the product rule
True
False
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