Question

Third derivative of $e^x\sin x$ at $x=0$ is

• A. $-2$
• B. $1$
• C. $2$
• D. $-1$

Answer 1

Answer: (C)

$2$

$y=e^{x}sinx$
$y^{{}^{\prime }}=e^{x}sinx+e^{x}cosx$
$y^{{}^{\prime \prime }}=y^{{}^{\prime }}+e^{x}cosx-e^{x}sinx$
$y^{{}^{\prime \prime }}=2y^{{}^{\prime }}-2y$
$y^{{}^{\prime \prime \prime }}=2y^{{}^{\prime \prime }}-2y^{{}^{\prime }}$
$y^{{}^{\prime \prime \prime }}{/}_{x=0}=4-2$
$=2$