Question

Find $\frac{d^{2}y}{d{x}^2}$ for $y=co{s}^{-1}x$.

Answer 1

$y=co{s}^{-1}xx=cosy1=-siny\frac{dy}{dx}\frac{dy}{dx}=-\frac{1}{siny}\frac{d^{2}y}{dx}=\frac{cosy}{si{n}^{2}y}\frac{dy}{dx}\frac{d^{2}y}{d{x}^2}=\frac{cosy}{si{n}^{2}y}\times \frac{-1}{siny}=-cotycose{c}^{2}y$