Chapter 2 - The Derivative - 2.9 Local Linear Approximation; Differentials - Exercises Set 2.9 - Page 181: 23

$8.9944$

The expression for $y$ can be written as: $y=x^{0.5}$ Now, $\dfrac{dy}{dx}=0.5x^{-0.5}$ $dy=0.5x^{-0.5} dx$ Next, we have: $dy=0.5 \times (81)^{-0.5}(-0.1)=-0.005556$ So, the new $y$ value is equal to $-0.005556+(81)^{0.5}=8.9944$