Implicit differentiation 2 (Basic)

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JPO AddMath 6 years ago

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Name	Status	Author	Last Modified
Implicit differentiation 2 (Basic)	draft	JPO AddMath	13/05/2019 10:47
Implicit differentiation 1 (Basic)	draft	JPO AddMath	13/05/2019 10:46

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Question statement

Find the gradient of the curve $\ln(y^\var{a})+\var{b}xy=\simplify{{c}*{b}}$ at the point $(\var{c},1)$ .

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			Name	Type	Generated Value

a	integer	5
b	integer	4
c	integer	-3

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"Part a)" → "Unnamed gap" - Correct answer
"Part b)" → "Unnamed gap" - Correct answer

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$\frac{dy}{dx}=$ Unnamed gap

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$\frac{d}{dx}(\ln(y^\var{a})+\var{b}xy)=\frac{d}{dx}(\simplify{{c}*{b}})$

$(\frac{1}{y^\var{a}}.\simplify{{a}y^{a-1}}).\frac{dy}{dx}+(\var{b}.1.y+\var{b}x.\frac{dy}{dx})=0$

$(\frac{\var{a}}{y}+\var{b}x)\frac{dy}{dx}=-\var{b}y$

$\frac{dy}{dx}=\frac{-\var{b}y}{\frac{\var{a}}y+\var{b}x}$

$\frac{dy}{dx}=\frac{-\var{b}y}{\frac{\var{a}}y+\var{b}x} \times \frac{y}{y}$

$\frac{dy}{dx}=\simplify{(-{b}y^2)/({a}+{b}x*y)}$

$\$

$\frac{dy}{dx} \bigg|_{(\var{c},1)}=\simplify{(-{b})/({a}+{b}*{c})}$

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This question is used in the following exam:

MID-TRIMESTER EXAM REVISION 2020 T3 by Maria Aneiros in Maria's workspace.

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JPO AddMath 6 years ago

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Implicit differentiation 2 (Basic)

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Taxonomy: mathcentre

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JPO AddMath 6 years ago

Error in variable testing condition

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Generated value: integer

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Gap-fill

Generated value: `integer`