If $y=\frac{1}{x+1}$, then $\frac{d^2y}{

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

If $y=\frac{1}{x+1}$, then $\frac{d^2y}{dx^2}$ at $x = 2$ is:

Options:

$\frac{2}{9}$

$\frac{3}{2}$

$\frac{2}{27}$

$\frac{3}{8}$

Correct Answer:

$\frac{2}{27}$

Explanation:

$y=\frac{1}{x+1}$ so differentiating y w.r.t. x

$⇒\frac{dy}{dx}=\frac{-1}{(x+1)^2}$ again differentiating w.r.t x

$⇒\frac{d^2y}{dx^2}=\frac{2}{(x+1)^3}$ so $\frac{d^2y}{dx^2}|_{x=2}=\frac{2}{(x+1)^3}=\frac{2}{3^3}$

$=\frac{2}{27}$