f(x,y)= x^3+x^2*y^3-2y^2

find fx(2,1) and fy(2,1)

First we need to calculate fx(x,y) and fy(x,y)

For fx(x,y) we differentiate with respect to x.

==> fx(x,y) = 3x^2 +(2y^3)x

Now substitute with (2,1)

==> fx(2,1)= 3(4) +2(1)2 = 12+4= 16

Now, for fy(x,y), we differentiate with respect to y

==> fy(x,y) = 3(x^2)y^2 -4y

Substitute with (2,1)

==> fy(2,1) = 3(4)(1) -4(1) = 12-4= 8

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