Question

If $f\left(x\right)=e^{x}g\left(x\right),g\left(0\right)=2,g^{\prime }\left(0\right)=1$, then $f^{\prime }\left(0\right)$ is

• A. $1$
• B. $3$
• C. $2$
• D. $0$

Answer 1

The correct option is B $3$

$f^{\prime }\left(x\right)=e^x{g}^{\prime }\left(x\right)+e^{x}g\left(x\right)$
$\Rightarrow f^{\prime }\left(0\right)=e^0.g^{\prime }\left(0\right)+e^{0}g\left(0\right)$
$=1.1+1.2$ $[\because \{g^{\prime }\left(0\right)=1$ and $g\left(0\right)=2\left\}\right]$
$=1+2=3$