Find d^2 y/dx^2 for the curve given by. x=2 cos theta and y=sin theta

Nelson Jennings 2022-07-28 Answered
Find ${d}^{2}y/d{x}^{2}$ for the curve given by
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Hassan Watkins
$\mathrm{cos}\left(\theta \right)=\frac{x}{2}$
$\mathrm{sin}\left(\theta \right)=y$
${\mathrm{cos}}^{2}\left(\theta \right)+{\mathrm{sin}}^{2}\left(\theta \right)=1$
$⇒\left(\frac{x}{2}{\right)}^{2}+{y}^{2}=1$
$\therefore {x}^{2}+4{y}^{2}=4$ [equation of curve]
Differentiating both sides with respect to x,
$2x+4×\left(2y\frac{dy}{dx}\right)=0$
$\therefore \frac{dy}{dx}=-\frac{x}{4y}$
$\therefore \frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(-\frac{x}{4y}\right)$
$⇒\frac{{d}^{2}y}{d{x}^{2}}=-\frac{y×1-x×\frac{dy}{dx}}{4{y}^{2}}$
Now, put value of dy/dx.