IMPLICIT DIFFERENTIATION 2

Authored by Greg Snelick

Mathematics

9th Grade - University

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MULTIPLE SELECT QUESTION

1 min • 2 pts

Which equations, if any, are written in implicit form?
(Check all that apply)

$y=4\ x-9$

$x^{\ 2}+y^{\ 2}=49$

$x\ y=16$

$y=\sqrt{36-x^{\ 2}}$

$y=\frac{25\ x}{x^{\ 2}-64}$

$x^{\ 2}+y^{\ 2}=1681$
Implicit Differentiation
$A\ x\ dB+C\ y\ dE=G$
$C\ y\ dE=-\ A\ x\ dB$
Submit $A,B,C,E,G$

(a)

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$x^{\ 2}+y^{\ 2}=1681$
Implicit Derivative
$\frac{dy}{dx}=-\ \frac{M}{N}$
Submit $M,N$

(a)

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$x^{\ 2}+y^{\ 2}=1681$
$Point\ \ P\left(-\ 40,9\right)$
Slope of local tangent at point $P$

$-\ \frac{40}{9}$

$-\ \frac{9}{40}$

$\frac{9}{40}$

$\frac{40}{9}$

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$x^{\ 2}+y^{\ 2}=1681$
$P\left(9,40\right)$
Slope of local tangent at point $P$

$-\ \frac{40}{9}$

$-\ \frac{9}{40}$

$\frac{9}{40}$

$\frac{40}{9}$

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$x\ y=36$
Implicit Differentiation
$x\ dA+y\ dB=C$
$x\ dA=-\ y\ dB$
Submit $A,B,C$

(a)

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$x\ y=36$
$\frac{dy}{dx}=-\ \frac{M}{N}$
Submit $M,N$

(a)

$x\ y=36$
$Point\ \ P\left(-\ 4,-\ 9\right)$
Slope of local tangent at point $P$

$-\ \frac{9}{4}$

$-\ \frac{4}{9}$

$\frac{4}{9}$

$\frac{9}{4}$

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$x\ y=36$
$Point\ \ P\left(12.3\right)$
Slope of local tangent at point $P$

$-\ 4$

$-\ \frac{1}{4}$

$\frac{1}{4}$

$4$

10.

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$x\ y+y+32=0$
Explicit form
$y=-\ \frac{A}{x+B}$
Submit $A,B$

(a)

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IMPLICIT DIFFERENTIATION 2

Which equations, if any, are written in implicit form? (Check all that apply)

x 2+y 2=1681x^{\ 2}+y^{\ 2}=1681x 2+y 2=1681 Implicit Differentiation A x dB+C y dE=GA\ x\ dB+C\ y\ dE=GA x dB+C y dE=G C y dE=− A x dBC\ y\ dE=-\ A\ x\ dBC y dE=− A x dB Submit A,B,C,E,GA,B,C,E,GA,B,C,E,G (a)

x 2+y 2=1681x^{\ 2}+y^{\ 2}=1681x 2+y 2=1681 Implicit Derivative dydx=− MN\frac{dy}{dx}=-\ \frac{M}{N}dxdy​=− NM​ Submit M,NM,NM,N (a)

x 2+y 2=1681x^{\ 2}+y^{\ 2}=1681x 2+y 2=1681 Point P(− 40,9)Point\ \ P\left(-\ 40,9\right)Point P(− 40,9) Slope of local tangent at point PPP

x 2+y 2=1681x^{\ 2}+y^{\ 2}=1681x 2+y 2=1681 P(9,40)P\left(9,40\right)P(9,40) Slope of local tangent at point PPP

x y=36x\ y=36x y=36 Implicit Differentiation x dA+y dB=Cx\ dA+y\ dB=Cx dA+y dB=C x dA=− y dBx\ dA=-\ y\ dBx dA=− y dB Submit A,B,CA,B,CA,B,C (a)

x y=36x\ y=36x y=36 dydx=− MN\frac{dy}{dx}=-\ \frac{M}{N}dxdy​=− NM​ Submit M,NM,NM,N (a)

x y=36x\ y=36x y=36 Point P(− 4,− 9)Point\ \ P\left(-\ 4,-\ 9\right)Point P(− 4,− 9) Slope of local tangent at point PPP

x y=36x\ y=36x y=36 Point P(12.3)Point\ \ P\left(12.3\right)Point P(12.3) Slope of local tangent at point PPP

x y+y+32=0x\ y+y+32=0x y+y+32=0 Explicit form y=− Ax+By=-\ \frac{A}{x+B}y=− x+BA​ Submit A,BA,BA,B (a)

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Which equations, if any, are written in implicit form?
(Check all that apply)

$x^{\ 2}+y^{\ 2}=1681$
Implicit Differentiation
$A\ x\ dB+C\ y\ dE=G$
$C\ y\ dE=-\ A\ x\ dB$
Submit $A,B,C,E,G$

(a)

$x^{\ 2}+y^{\ 2}=1681$
Implicit Derivative
$\frac{dy}{dx}=-\ \frac{M}{N}$
Submit $M,N$

(a)

$x^{\ 2}+y^{\ 2}=1681$
$Point\ \ P\left(-\ 40,9\right)$
Slope of local tangent at point $P$

$x^{\ 2}+y^{\ 2}=1681$
$P\left(9,40\right)$
Slope of local tangent at point $P$

$x\ y=36$
Implicit Differentiation
$x\ dA+y\ dB=C$
$x\ dA=-\ y\ dB$
Submit $A,B,C$

(a)

$x\ y=36$
$\frac{dy}{dx}=-\ \frac{M}{N}$
Submit $M,N$

(a)

$x\ y=36$
$Point\ \ P\left(-\ 4,-\ 9\right)$
Slope of local tangent at point $P$

$x\ y=36$
$Point\ \ P\left(12.3\right)$
Slope of local tangent at point $P$

$x\ y+y+32=0$
Explicit form
$y=-\ \frac{A}{x+B}$
Submit $A,B$

(a)