Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If $x^2+y^2=1$, then

Options:

$y y''-2\left(y'\right)^2+1=0$

$y y''+\left(y'\right)^2+1=0$

$y y''+\left(y'\right)^2-1=0$

$y y''+2\left(y'\right)^2+1=0$

Correct Answer:

$y y''+\left(y'\right)^2+1=0$

Explanation:

We have,

$x^2+y^2=1$

Differentiating w.r.t. x, we get

$2 x+2 y y'=0 \Rightarrow x+y y'=0$

Again differentiating w. r. t. x, we get

$1+\left(y'\right)^2+y y''=0$