Given , ¦nd by implicit differentiation.
Select one:
a.
b.
c.
d.
5x2 + 2y3 = 10 dy
dx
5 3
x 2y
−
5 3
x 2y
x 2y 3−5
x 2y9/5/2021 Graded Exam 2
https://moodle.straighterline.com/mod/quiz/review.php?attempt=4
...
Given , ¦nd by implicit differentiation.
Select one:
a.
b.
c.
d.
5x2 + 2y3 = 10 dy
dx
5 3
x 2y
−
5 3
x 2y
x 2y 3−5
x 2y9/5/2021 Graded Exam 2
https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 2/11
Question 2
Correct
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Question 3
Correct
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of 5.00
Question 4
Correct
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of 5.00
Compute the derivative of the function .
Select one:
a.
b.
c.
d.
What is the derivative of the function ?
Select one:
a.
b.
c.
d. \( 3x^2+2e^x \)
What is the derivative of the function
\( f(x)= \sqrt{x} \)?
Select one:
a. \( \displaystyle \frac{1}{\sqrt{x}} \)
b. \( \displaystyle \frac{1}{2\sqrt{x}} \)
c. \( \displaystyle \frac{2}{\sqrt{x}} \)
d. \( \displaystyle \frac{1}{2} \)
f(x) = sec x
cos x
− tan x sec x
sin2 x
tan x sec x
f(x) = x3 + 2e2x
3x2 + 4e2x
3x2 + 2e2x
3x2 + 2e29/5/2021 Graded Exam 2
https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 3/11
Question 5
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Question 6
Correct
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Evaluate the following as true or false.
If \( f(x) = x^N \), where N is some number, then \( f'(x) = Nx \).
Select one:
a. true
b. false
The width \( x \) of a rectangle is decreasing at \( 3\, \hbox{cm/s} \), and its length
\( y \) is increasing at \( 5\, \hbox{cm/s} \). At what rate is its area \( A \) changing
when \( x = 10\, \hbox{ cm} \) and \( y = 15\, \hbox{ cm} \)?
Select one:
a. \( 1/5\, \hbox{cm}^2\hbox{/s} \)
b. \( -5\, \hbox{cm}^2\hbox{/s} \)
c. \( 5\, \hbox{cm}^2\hbox{/s} \)
d. none of the above9/5/2021 Graded Exam 2
https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 4/11
Question 7
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Question 8
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Compute the derivative of the function
\( f(x) = (-3x^4+5x^2-\sqrt{x}+3)\,(x^{-2}-6x) \).
Select one:
a. \( \bigg( -12\,x^3+10x+ \displaystyle \frac{1}{2}x^{-\frac{1}{2}} \bigg)
(x^{-2}-6x)\\ \quad\quad\quad\quad\quad +(-3x^4+5x^2-\sqrt{x}+3)\,
(-2x^{-3}-6) \)
b. \( \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{1}{2}} \bigg) \,
(x^{-2}-6x)\\ \quad\quad\quad\quad\quad+(-3x^4+5x^2-\sqrt{x}+3)\,
(-2x^{-3}-6) \)
c. \( \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{3}{2}} \bigg)
(x^{-2}-6x)\\ \quad\quad\quad\quad\quad +(-3x^4+5x^2-\sqrt{x}+3)\,
(-2x^{-3}-6) \)
d. \( \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{3}{2}} \bigg)
(-2x^{-3}-6) \)
Find all points on \( xy=e^{xy} \) where the tangent line is horizontal.
Select one:
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