WAEC 2023 · Paper 1 · Q13

Given that $y^2 + xy = 5$ , find $\dfrac{dy}{dx}$ .

Worked solution (try it first)

Differentiate each term with respect to $x$ .
By the chain rule, $y^2$ gives $2y\dfrac{dy}{dx}$ .
By the product rule, $xy$ gives $y + x\dfrac{dy}{dx}$ .
So $2y\dfrac{dy}{dx} + y + x\dfrac{dy}{dx} = 0$ .
Factorise: $\dfrac{dy}{dx}(2y + x) = -y$ , so $\dfrac{dy}{dx} = \dfrac{-y}{2y + x}$ , option B.