Chapter 2 - Differentiation - 2.6 Exercises - Page 153: 1

a) dy/dt = 3/4 b) dx/dt = 20

$ y = \sqrt(x) $ $\frac{d}{dt} (y) = \frac{d}{dt} \sqrt(x) $ $1 \frac{dy}{dt} = \frac{1}{2\sqrt(x)}\frac{dx}{dt}$ a) Find dy/dt when x = 4 and dx/dt = 3 then $1 \frac{dy}{dt} = \frac{1}{2\sqrt(4)}(3) = (1/4)*3 = 3/4 $ b) Find dx/dt when x = 25 and dy/dt = 2 $2 = \frac{1}{2\sqrt(25)}\frac{dx}{dt}$ $\frac{dx}{dt} = 4(5) = 20 $