If x^2 + 2xy + 3y^2 = 1, what is dy/dx?

Derivatives & Second-Order Derivatives · Question 32 of 96

Question 32

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If $x^2 + 2xy + 3y^2 = 1$ , what is $\frac{dy}{dx}$ ?

\frac{- x - 3 y}{x + y}

Correct answerYour answer

- \frac{x}{3 y}

Correct answerYour answer

\frac{x + y}{x + 3 y}

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\frac{- x - y}{x + 3 y}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$2x + 2\left(y + x\frac{dy}{dx}\right) + 6y\frac{dy}{dx} = 0$ : the term $2xy$ needs the product rule.
$(2x + 6y)\frac{dy}{dx} = -(2x + 2y)$ , so $\frac{dy}{dx} = -\frac{x + y}{x + 3y}$ .

Worth noting

$-\frac{x}{3y}$ differentiates $2xy$ as if $y$ were a constant, dropping the product rule.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.