Here is the work for this hy f ay 2a2y3 hb 6a2b2 h y f a y 2 a 2 y 3 h b 6 a 2 b 2. If a real-valued function f is continuous on the closed and bounded set D in R 2 then f must attain a maximum and a minimum each. Example 1 Find the partial derivatives f x and f y if fx y is given by fxy x2 y 2 x y Solution to Example 1.
Here is the work for this hy f ay 2a2y3 hb 6a2b2 h y f a y 2 a 2 y 3 h b 6 a 2 b 2.
Use parentheses if necessary e. F x 2 x 2 2 3 8 x 2. The derivative of any constant number such as 4 is 0. In calculating the partial derivative you are just changing the value of one variable while keeping others constant.