(a)[4]
Show that the result is $\displaystyle \frac{dy}{dx} = \frac{y^2 - y e^x}{x e^x + 2y}$.
(b)[2]
Find the gradients of the tangents to the curve at $x = 0$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is defined by $xy + y^2 e^{-x} = 4$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using the product rule, differentiating $xy$ gives $y+x\frac{dy}{dx}$” …
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