Answer
The estimated partial derivatives at $P$ are
${f_x} \simeq - 2.5$
${f_y} \simeq 3.75$
Work Step by Step
1. Estimate ${f_x}$ at $P$
From Figure 10 we get $\Delta f = 9 - 12 = - 3$ and estimated $\Delta x \simeq 1.2$.
${f_x} \approx \frac{{\Delta f}}{{\Delta x}} \simeq \frac{{ - 3}}{{1.2}} \simeq - 2.5$
2. Estimate ${f_y}$ at $P$
From Figure 10 we get $\Delta f = 15 - 12 = 3$ and estimated $\Delta y \simeq 0.8$.
${f_y} \approx \frac{{\Delta f}}{{\Delta y}} \simeq \frac{3}{{0.8}} \simeq 3.75$
