Chapter 3 - Section 3.9 - Related Rates - 3.9 Exercises - Page 249: 9

(a) $\frac{dy}{dt} = 1$ (b) $\frac{dx}{dt} = 25$

(a) $y = \sqrt{2x+1}$ $\frac{dy}{dx} = \frac{1}{\sqrt{2x+1}}$ $\frac{dy}{dx}~\frac{dx}{dt} = \frac{1}{\sqrt{2x+1}}~\frac{dx}{dt}$ $\frac{dy}{dt} = \frac{1}{\sqrt{2x+1}}~\frac{dx}{dt}$ $\frac{dy}{dt} = \frac{1}{\sqrt{(2)(4)+1}}~(3)$ $\frac{dy}{dt} = 1$ (b) $y = \sqrt{2x+1}$ $\frac{dy}{dx} = \frac{1}{\sqrt{2x+1}}$ $\frac{dy}{dx}~\frac{dx}{dt} = \frac{1}{\sqrt{2x+1}}~\frac{dx}{dt}$ $\frac{dy}{dt} = \frac{1}{\sqrt{2x+1}}~\frac{dx}{dt}$ $\frac{dx}{dt} = (\frac{dy}{dt})~\sqrt{2x+1}$ $\frac{dx}{dt} = (5)~\sqrt{(2)(12)+1}$ $\frac{dx}{dt} = 25$