"Use difference quotients with delta(x)=0.1 and delta(y)=0.1 to estimate fx(1,3) and fy(1,3) where f(x,y)=e^(-x)sin(y)."

Question

I don't know how to solve this problem. Could someone walk me through it? Thank you so much!

Answer 1

a) find the partial derivatives of each, and just plug in 1 for x and 3 for y (values should be close to 0)/

b) in using the difference quotients, take the limit as h approaches infinity of both each derivative, plugging in 0.1 for x and y in each one. It's better that you think critically about how the definition of the derivatives applies not only in 2D, but in 3-space as well. You'll gain a better intuition.