Q.If $y = \sin x$, find $\dfrac{d^{2}y}{dx^{2}}$.

Differentiate twice using the trigonometric standard derivatives. …

First derivative: $\dfrac{dy}{dx}=\dfrac{d}{dx}(\sin x)=\cos x$.

Second derivative — differentiate $\cos x$:

$\frac{d^2y}{dx^2}=\frac{d}{dx}(\cos x)=-\sin x.$ …

Do not forget the minus sign when differentiating $\cos x$: $\frac{d}{dx}\cos x=-\sin x$. The sec …