Practicing Success
If $y=\frac{1}{\sqrt{1+x^2}-x}$, then the value of $\left(1+x^2\right)^{\frac{3}{2}} \cdot \frac{d^2 y}{d x^2}$ is |
x x2 - 1 \(\sqrt{1+x^2} - 1\) 1 |
1 |
$y=\frac{1}{\sqrt{1+x^2}-x}×\frac{\sqrt{1+x^2}+x}{\sqrt{1+x^2}+x}⇒\frac{\sqrt{1+x^2}+x}{1}$ $∴\frac{dy}{dx}=\frac{1}{2\sqrt{1+x^2}}×2x+1=\frac{y}{\sqrt{1+x^2}}$ $=\frac{d^2y}{dx^2}=\frac{\sqrt{1+x^2}\frac{dy}{dx}-y\frac{1}{2\sqrt{1+x^2}}.2x}{(1+x^2)}$ $⇒(1+x^2)^{\frac{3}{2}}=y(\sqrt{1+x^2}-x)=1$ Option 4 is correct. |