Question

$\frac{d^{2}x}{d{y}^2}$ equals

• A. ${\left(\frac{d^{2}y}{d{x}^2}\right)}^{-1}$
• B. $-{\left(\frac{d^{2}y}{d{x}^2}\right)}^{-1}{\left(\frac{dy}{dx}\right)}^{-3}$
• C. ${\left(\frac{d^{2}y}{d{x}^2}\right)}^{-1}{\left(\frac{dy}{dx}\right)}^{-2}$
• D. ${(-\frac{d^{2}y}{d{x}^2})}^{-1}{\left(\frac{dy}{dx}\right)}^{-2}$

Answer 1

The correct option is A ${\left(\frac{d^{2}y}{d{x}^2}\right)}^{-1}$

We have,

$\frac{d^{2}x}{d{y}^2}$

$={\left(\frac{d^{2}x}{d{y}^2}\right)}^1$

$=\frac{1}{{\left(\frac{d^{2}x}{d{y}^2}\right)}^{-1}}$

$={\left(\frac{d^{2}y}{d{x}^2}\right)}^{-1}$

Hence, this is the answer.