Respuesta :

[tex]\bf h(x)=\cfrac{f(x)}{g(x)}\impliedby \textit{let us use the quotient rule}\\\\ -----------------------------\\\\ \cfrac{dh}{dx}=\left. \cfrac{\frac{df}{dx}g(x)-f(x)\frac{dg}{dx}}{[g(x)]^2}\right|_{x=7}\quad \begin{cases}f'(7)=14\\\\ f(7)=0\\\\ g'(7)=\frac{1}{7}\\\\ g(7)=1 \end{cases}\implies \cfrac{dh}{dx}=\cfrac{14\cdot 1-0\cdot \frac{1}{7}}{[1]^2} \\\\\\ \cfrac{dh}{dx}=\cfrac{14}{1}\implies \cfrac{dh}{dx}=14 [/tex]