Partial derivative with one variable
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fx(x, y)
Scenario: Solve for fx(x,y) with the function below.
We're evaluating this derivative with respect to x.
In other words... take the derivative of f(x, y) treating x as a variable and y as a constant!
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: fx(x, y) = 6xy + 10xy3
fy(x, y)
Scenario: Solve for fy(x,y) with the function below.
We're evaluating this derivative with respect to y.
In other words... take the derivative of f(x, y) treating y as a variable and x as a constant!
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: fy(x, y) = 3x2 + 15x2y2