Read the two statements and choose the correct option. I. For y^2 = 4x, dy/dx = 2/y. II. For x^2 - y^2 = 1, dy/dx = -x/y.

Derivatives & Second-Order Derivatives · Question 42 of 96

Question 42

MediumOriginal question

Read the two statements and choose the correct option.
I. For $y^2 = 4x$ , $\frac{dy}{dx} = \frac{2}{y}$ .
II. For $x^2 - y^2 = 1$ , $\frac{dy}{dx} = -\frac{x}{y}$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $2y\frac{dy}{dx} = 4$ , so $\frac{dy}{dx} = \frac{2}{y}$ . True.
II: $2x - 2y\frac{dy}{dx} = 0$ , so $\frac{dy}{dx} = \frac{x}{y}$ , with no minus sign. False.

Worth noting

II copies the circle's slope; the minus in front of $y^2$ changes the sign.

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

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