Chapter 12.5, Problem 53E

(a)

To determine

To show: That $\frac{d}{dx}\ln h\left(x\right)=\frac{v\left(x\right)u^{\prime }\left(x\right)}{u\left(x\right)}+\left(\ln u\left(x\right)\right)v^{\prime }\left(x\right)$.

(b)

To determine

To show: That $\frac{d}{dx}h\left(x\right)=u{\left(x\right)}^{v\left(x\right)}\left[\frac{v\left(x\right)u^{\prime }\left(x\right)}{u\left(x\right)}+\left(\ln u\left(x\right)\right)v^{\prime }\left(x\right)\right]$.