Question

Find fx(x,y), fy(x,y), fx(1,3), and fy(-2,4) for the given function. If 

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥ଷ𝑦ଶ − 𝑥ଶ𝑦ଷ + 4𝑥 + 9

Answer 1

Given f(x,y) = 3x²y - xy² + 4x + 9

Now f_x(x,y) = (d/dx)(3x²y - xy² + 4x + 9)

= 6xy - y² + 4

Now f_x(1,3) = 6*1*3 - 3² + 4 = 13

Now f_y(x,y) = (d/dy)(3x²y - xy² + 4x + 9)

= 3x² - 2xy

Now f_y(-2,4) = 3(-2)² - 2(-2)(4) = 28