Chapter 14.1, Problem 3E

To determine

Find the value of $f_x\left(1,3\right)$ and $f_y\left(1,3\right)$ for the function $f\left(x,y\right)=e^{-x}\sin y$ using difference quotients where $\Delta x=0.1\text{ and }\Delta y=0.1$ and then give better estimates by using $\Delta x=0.01\text{ and }\Delta y=0.01$ .