Partial derivative with two variables
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fxy(x, y)
Scenario: Solve for fxy(x,y) with the function below.
We're evaluating this derivative with respect to x... then with respect to y.
In other words... take the derivative of f(x, y) treating x as a variable and y as a constant... and then do the opposite!
Remember: we're treating y as a constant, so pull it out front before taking the derivative of the x term! (Constant Multiple Rule)
Answer: fxy(x, y) = 6x + 30xy2
fyx(x, y)
Scenario: Solve for fyx(x,y) with the function below.
We're evaluating this derivative with respect to y... then with respect to x.
In other words... take the derivative of f(x, y) treating y as a variable and x as a constant... and then do the opposite!
Remember: we're treating x as a constant, so pull it out front before taking the derivative of the y term! (Constant Multiple Rule)
Answer: fy,x(x, y) = 6x + 30xy2