Question

(1 point) Find the partial derivatives of the function f(x,y)=xye^ −6y f x​(x,y)f y​ (x,y)f xy​ (x,y)f yx​ (x,y)= ​

Answer 1

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!