given ( y = sqrt{x} ). find ( \frac{dx}{dt} ) when ( y = 4 ) and ( \frac{dy}{dt} = 1.95 ).\n\n(…

given ( y = sqrt{x} ). find ( \frac{dx}{dt} ) when ( y = 4 ) and ( \frac{dy}{dt} = 1.95 ).\n\n( \frac{dx}{dt} = square ) (simplify your answer.)

given ( y = sqrt{x} ). find ( \frac{dx}{dt} ) when ( y = 4 ) and ( \frac{dy}{dt} = 1.95 ).\n\n( \frac{dx}{dt} = square ) (simplify your answer.)

Answer

Explanation:

Step1: Express (x) in terms of (y)

Given (y = \sqrt{x}), we can rewrite it as (x=y^{2}).

Step2: Differentiate (x) with respect to (t)

Using the chain - rule (\frac{dx}{dt}=2y\frac{dy}{dt}).

Step3: Substitute the given values of (y) and (\frac{dy}{dt})

When (y = 4) and (\frac{dy}{dt}=1.95), we substitute these values into the equation (\frac{dx}{dt}=2y\frac{dy}{dt}). So (\frac{dx}{dt}=2\times4\times1.95). First, calculate (2\times4 = 8), then (8\times1.95=15.6).

Answer:

(15.6)