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Computing Derivatives
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Home
/
Calculus
/
Computing Derivatives
/
Module Flashcards
/
The Rules of the Game Flashcards
TABLE OF CONTENTS
Intro
Topics
Examples
Exercises
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What's in a Slope?
Embrace Your Inner Calculator
The Rules of the Game
True or False
Flashcards
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Computing Derivatives: The Rules of the Game True or False
1.
Let
h
(
x
) = e
^{{3x + 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
= 4t
^{2}
+ 3 and
r
= cos
s
, then to find the derivative of
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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