Find the partial derivative indicated Assume the variables a

Find the partial derivative indicated. Assume the variables are restricted to a domain on which the function is defined. z = 3x2y5 - y5 15 xy - 9. zy =

Solution

z = (3x² - 1)/3 * y⁵/(5xy - 3)

z_y = (3x² - 1)/3 * [(5xy - 3)*5y⁴ - y⁵ * 5x]/(5xy - 3)²

= 5(3x² - 1)y⁴/3 * (4xy - 3)/(5xy - 3)²