Successive derivatives of standard functions for JEE

Formula

\[\frac{d^2}{dx^2}(\sin x)=-\sin x,\quad \frac{d^2}{dx^2}(\cos x)=-\cos x,\quad \frac{d^2}{dx^2}(e^x)=e^x,\quad \frac{d^2}{dx^2}(\ln x)=-\frac1{x^2}\]

Conditions: At points where defined; for \(\ln x\), \(x>0\).

Direct second derivative evaluation.