Help with calculus differentials please!!?

Question

Use difference quotients with Δx=0.1 and Δy=0.1 to estimate fx(1,1) and fy(1,1) where
f(x,y)=e−xsin(y).

need to find fx(1,1) and fy(1,1)

I am so lost on the difference quotient..

Answer 1

Step 1 :

Definition :

The x - partial derivative and y - partial derivative of   at are

.

Step 2 :

The function is .

Difference quotients are .

Find .

The function is .

Thus, .

Step 3 :

Find .

The function is .

Thus, .

Solution :

.

.