Question

Let $f\left(x\right)=\{\begin{array}{cc}\sin x,& forx\ge 0\\ 1-\cos x,& forx<0\end{array}$ and $g\left(x\right)=e^x$. Then $\left(gof{)}^{\prime }\right(0)$ is

Answer 1

Given, $f\left(x\right)=\{\begin{array}{cc}\sin x,& forx\ge 0\\ 1-\cos x,& forx<0\end{array}$

$g\left(x\right)=e^x$

For $x\ge 0$; $gof\left(x\right)=e^{sinx}$

$go{f}^{\prime }\left(x\right)=e^{\sin x}\cos x$

$go{f}^{\prime }\left(0\right)=e^0\times 1=1$