Find the first partial derivatives of the function fx y y3

Find the first partial derivatives of the function. f(x, y) = y3 4xy

Solution

For partial derivatives with respect to x, differentiate only the terms which have the x in them and treat rest of variables as constant.

For partial derivatives with respect to y, differentiate only the terms which have the y in them treat rest of variables as constant.

df/dx = -4y

df/dy = 3y² - 4x