$$ f_x(1,2)= -164$$
Work Step by Step
Since $ f(x,y)=3x^2y+4x^3y^2-7xy^5$, then we have $$ f_x=6xy+12x^2y^2-7y^5.$$ Hence, we get $$ f_x(1,2)=6(2)+12(4)-7(2^5)=-164$$
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