#### Problem 59E

59. Suppose that

$$\begin{array}{llll} f(1)=2 & f^{\prime}(1)=3 & f(2)=1 & f^{\prime}(2)=2 \\ g(1)=3 & g^{\prime}(1)=1 & g(2)=1 & g^{\prime}(2)=4 \end{array}$$

(a) If $S(x)=f(x)+g(x)$, find $S^{\prime}(1)$.

(b) If $P(x)=f(x) g(x)$, find $P^{\prime}(2)$.

(c) If $Q(x)=f(x) / g(x)$, find $Q^{\prime}(1)$.

(d) If $C(x)=f(g(x))$, find $C^{\prime}(2)$.