second partial derivatives

Question

Find the second partial derivatives of f(x,y)=4x³y-7xy².

Answer 1

Function .

The above function have two variables, we can differentiate with respect to x and y.

Here we have four cases and those are denoted as

Now find .

While differentiating partially with respect to x , y  treated as constant.

.

find .

While differentiating partially with respect to y , x  treated as constant.

find .

 find .

.

The second partial derivatives are

, , .