Answer to Question #205313 in Calculus for Touseef

Question #205313

find fx (x,y),fy(x,y),f,(1,3),and fy (-2,4) for the given function. If z=f(x,y)=3x3y2-x2y3+4x+9




1
Expert's answer
2021-06-11T18:35:42-0400
𝑧=𝑓(π‘₯,𝑦)=3π‘₯3𝑦2βˆ’π‘₯2𝑦3+4π‘₯+9𝑧 = 𝑓(π‘₯, 𝑦) = 3π‘₯^3𝑦^2 βˆ’ π‘₯^2𝑦^3 + 4π‘₯ + 9


fx(x,y)=9x2y2βˆ’2xy3+4f_x(x, y)=9x^2y^2-2xy^3+4

fy(x,y)=6x3yβˆ’6x2y2f_y(x, y)=6x^3y-6x^2y^2


fx(1,3)=9(1)2(3)2βˆ’2(1)(3)3+4=29f_x(1, 3)=9(1)^2(3)^2-2(1)(3)^3+4=29

fy(βˆ’2,4)=6(βˆ’2)3(4)βˆ’6(βˆ’2)2(4)2=βˆ’576f_y(-2, 4)=6(-2)^3(4)-6(-2)^2(4)^2=-576


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