Find dy/dx at (4, 1) for the curve √(x) + √(y) = 3.

Derivatives & Second-Order Derivatives · Question 44 of 96

Question 44

MediumOriginal question

Find $\frac{dy}{dx}$ at $(4, 1)$ for the curve $\sqrt{x} + \sqrt{y} = 3$ .

-2

Correct answerYour answer

- \frac{1}{2}

Correct answerYour answer

- \frac{1}{4}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\frac{1}{2\sqrt{x}} + \frac{1}{2\sqrt{y}}\frac{dy}{dx} = 0$ , so $\frac{dy}{dx} = -\frac{\sqrt{y}}{\sqrt{x}}$ .
At $(4, 1)$ : $-\frac{1}{2}$ .

Worth noting

$-2$ is $-\frac{\sqrt{x}}{\sqrt{y}}$ , the ratio turned upside down.

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

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