Final answer:
The partial derivatives of f(x,y)=xye−6y are fx(x,y)=ye−6y and fy(x,y)=(x−6xy)e−6y.
Step-by-step explanation:
To find the partial derivatives of the function f(x,y)=xye−6y, we'll compute the partial derivatives with respect to x and y.
The function is given by:
f(x,y)=xye−6y
Now, let's find the partial derivatives:
Partial derivative with respect to x, denoted as fx(x,y):
fx(x,y)=ye−6y
Partial derivative with respect to y, denoted as fy(x,y):
fy(x,y)=(x−6xy)e−6y
These are the partial derivatives of the given function f(x,y)=xye−6y with respect to x and y.
If you have any specific points at which you'd like to evaluate these derivatives, or if you have additional questions, feel free to ask!