Contoh 1

$y=\sin (4x+5)$

${\displaystyle \frac{dy}{dx}}=y^{\prime }=4.\cos (4x+5)$

${\displaystyle \frac{d^{2}y}{d{x}^2}}=y^{″}=-4.4.\sin (4x+5)=-16.\sin (4x+5)$

Contoh 2

$y=\cos (3x+1)$

${\displaystyle \frac{dy}{dx}}=y^{\prime }=-3.\sin (3x+1)$

${\displaystyle \frac{d^{2}y}{d{x}^2}}=y^{″}=-3.3.\cos (3x+1)=-9.\cos (3x+1)$

Contoh 3

$y=4\sin (2t-10)$

${\displaystyle \frac{dy}{dx}}=y^{\prime }=4.2.\cos (2t-10)=8.\cos (2t-10)$

${\displaystyle \frac{d^{2}y}{d{x}^2}}=y^{″}=8.-2.\sin (2t-10)=-16.\sin (2t-10)$

Contoh 4

$y=2\cos (3t+20)$

${\displaystyle \frac{dy}{dx}}=y^{\prime }=2.-3.\sin (7t+30)=-6.\sin (3t+20)$

${\displaystyle \frac{d^{2}y}{d{x}^2}}=y^{″}=-6.3.\cos (3t+20)=-18.\cos (3t+20)$