Edexcel C4 2010 June — Question 3 7 marks

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2010
SessionJune
Marks7
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TopicImplicit equations and differentiation
TypeFind dy/dx at a point
DifficultyStandard +0.3 This is a straightforward implicit differentiation question requiring application of the product rule and chain rule to find dy/dx, then substitution of given coordinates. It's slightly easier than average because it's a direct application of a standard technique with clear steps and no conceptual surprises.
Spec1.07s Parametric and implicit differentiation
3. A curve \(C\) has equation $$2 ^ { x } + y ^ { 2 } = 2 x y$$ Find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point on \(C\) with coordinates \(( 3,2 )\).
AnswerMarks Guidance
\(\frac{d}{dx}(2^x) = \ln 2.2^x\)B1
\(\ln 2.2^x + 2y\frac{dy}{dx} = 2y + 2x\frac{dy}{dx}\)M1 A1 A1
Substituting \((3, 2)\): \(8\ln 2 + 4\frac{dy}{dx} = 4 + 6\frac{dy}{dx}\)M1
\(\frac{dy}{dx} = 4\ln 2 - 2\)M1 A1 Accept exact equivalents 
| $\frac{d}{dx}(2^x) = \ln 2.2^x$ | B1 | |
| $\ln 2.2^x + 2y\frac{dy}{dx} = 2y + 2x\frac{dy}{dx}$ | M1 A1 | A1 |
| Substituting $(3, 2)$: $8\ln 2 + 4\frac{dy}{dx} = 4 + 6\frac{dy}{dx}$ | M1 | |
| $\frac{dy}{dx} = 4\ln 2 - 2$ | M1 A1 | Accept exact equivalents |

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3. A curve $C$ has equation

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

Find the exact value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ at the point on $C$ with coordinates $( 3,2 )$.\\

\hfill \mbox{\textit{Edexcel C4 2010 Q3 [7]}}
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