Find dy/dx at (1, 2) for the curve x^2 + xy + y^2 = 7.

Derivatives & Second-Order Derivatives · Question 37 of 96

Question 37

MediumOriginal question

Find $\frac{dy}{dx}$ at $(1, 2)$ for the curve $x^2 + xy + y^2 = 7$ .

- \frac{8}{5}

Correct answerYour answer

- \frac{5}{4}

Correct answerYour answer

- \frac{4}{5}

Correct answerYour answer

\frac{4}{5}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Differentiate every term with respect to $x$ , treating $y$ as a function of $x$ , so $y$ terms pick up $\frac{dy}{dx}$ .
Solving for it: $\frac{dy}{dx} = \frac{- 2 x - y}{x + 2 y}$ .
At $(1, 2)$ this is $- \frac{4}{5}$ .

Worth noting

$- \frac{5}{4}$ is $\frac{dx}{dy}$ , the reciprocal.

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

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