Answer to Question #206168 in Calculus for shaheryar

Question

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

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥³y² - 𝑥²y³ + 4𝑥 + 9

Answer 1

Z=f(x,y)=3x³y²-x²y³+4x+9

f_x(x,y)=9x²y²-2xy³+4

f_y(x,y)=6x³y-3x²y²

f_x(1,3)=9(1)²(3)²-2(1)(3)³+4

=9*1*9-2*27+4

= 81-54+4

=31

f_y(-2,4)= 6(-2)³4-3(-2)²4²

=6*-8*4-3*4*16

=-192-192

=-384