Find dy/dx at (3, 4) for the curve xy = 12.

Derivatives & Second-Order Derivatives · Question 30 of 96

Question 30

EasyOriginal question

Find $\frac{dy}{dx}$ at $(3, 4)$ for the curve $xy = 12$ .

- \frac{4}{3}

Correct answerYour answer

- \frac{3}{4}

Correct answerYour answer

- \frac{1}{3}

Correct answerYour answer

\frac{4}{3}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

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: $\frac{dy}{dx} = - \frac{y}{x}$ .
At $(3, 4)$ this is $- \frac{4}{3}$ .

Worth noting

$- \frac{3}{4}$ 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.