Question

For the curve $xy=c^2$ the subnormal at any point varies as
[Karnataka CET 2003]

• A. $x^2$
• B. $x^3$
• C. $y^2$
• D. $y^3$

Answer 1

The correct option is D $y^3$

Let y = $f\left(e^x\right)\Rightarrow \frac{dy}{dx}=f^{\prime }\left(e^x\right)e^x$
$\frac{d^{2}y}{d{x}^2}=f^{\prime }\left(e^x\right).e^x.e^x+e^x.f^{\prime }\left(e^x\right)=f^{\prime }\left(e^x\right).e^{2x}+f^{\prime }\left(e^x\right).e^x.$