Chapter 2, Problem 28RE

In each part, evaluate the expression given that $f\left(1\right)=1,g\left(1\right)=-2,f^{\prime }\left(1\right)=3$ , and $g^{\prime }\left(1\right)=-1$ .

(a) ${\left.\frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]\right|}_{x=1}$

(b) ${\left.\frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]\right|}_{x=1}$

(c) ${\left.\frac{d}{dx}\left[\sqrt{f\left(x\right)}\right]\right|}_{x=1}$

(d) $\frac{d}{dx}\left[f\left(1\right)g^{\prime }\left(1\right)\right]$