Assume that there exists a function L : (0; ) R such that L (x) =

Question:

Assume that there exists a function L : (0; ∞) → R such that Lʹ (x) = 1/x for x > 0. Calculate the derivatives of the following functions:
(a) f(x) := L(2x + 3) for x > 0.
(b) g(x) := (L(x2))3 for x > 0;
(c) h(x) := L(ax) for a > 0, x > 0,
(d) k(x) := L(L(x)) when L(x) > 0, x > 0.