Second derivative $f^{\prime \prime}(x)=\frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(\frac{d y}{d x}\right)=\frac{d y^{\prime}}{d x}=y^{\prime \prime}=D^{2}(f)(x)=D_{x}^{2} f(x)$ Third derivative $y^{\prime \prime \prime}=\frac{d y^{\prime \prime}}{d x}=\frac{d^{3} y }{ d x^{3}}$ n-th derivative $y^{(n)}=\frac{d}{d x} y^{(n-1)}=\frac{d^{n} y}{d x^{n}}=D^{n} y$ --- How to Read the Symbols for Derivatives | Symbol | Language | |--------|----------| |$y^\prime$|"y prime"| |$y^{\prime\prime}$|"y double prime"| |$\frac{d^{2} y}{d x^{2}}$|"d squared y dx squared"| |$y^{\prime \prime \prime}$|"y triple prime"| |$y^{(n)}$|"y super n"| |$\frac{d^{n} y}{d x^{n}}$|"d to the n of y by dx to the n"| |$D^{n}$|"D to the n"|