Question

lf $x=e^t\cos t,y=e^t\sin t$ then $\frac{d^{2}y}{d{x}^2}$ at $t=0$ is

• A. $0$
• B. $2$
• C. $2/e$
• D. $1$

Answer 1

The correct option is B $2$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{e^t\sin t+e^t\cos t}{e^t\cos t+e^t\sin t}$

$\frac{dy}{dx}=\frac{y+x}{x-y}$

$\frac{d^{2}y}{d{x}^2}=\frac{(\frac{dy}{dx}+1)(x-y)-(1-\frac{dy}{dx})(y+x)}{{(x-y)}^2}$

$\frac{d^{2}y}{d{x}^2}{/}_{t=0}=2$