Chapter 2.4, Problem 29ES

In parts (a)-(d), $F\left(x\right)$ is expressed in terms of $f\left(x\right)$ and $g\left(x\right)$ . Find $F^{\prime }\left(2\right)$ given that $f\left(2\right)=-1,f^{\prime }\left(2\right)=,g\left(2\right)=1$ , and $g^{\prime }\left(2\right)=-5$ .

(a) $F\left(x\right)=5f\left(x\right)+2g\left(x\right)$

(b) $F\left(x\right)=f\left(x\right)-3g\left(x\right)$

(c) $F\left(x\right)=f\left(x\right)g\left(x\right)$

(d) $F\left(x\right)=f\left(x\right)/g\left(x\right)$