Math  /  Calculus

QuestionFind the second-order partial derivative. Find fxyf_{x y} when f(x,y)=10x2y47x3y5f(x, y)=10 x^{2} y^{4}-7 x^{3} y^{5}. 160xy321x2y4160 x y^{3}-21 x^{2} y^{4} 80xy321x2y480 x y^{3}-21 x^{2} y^{4} 80xy3105x2y480 x y^{3}-105 x^{2} y^{4} 160xy3105x2y4160 x y^{3}-105 x^{2} y^{4}

Studdy Solution
Apply the power rule for differentiation:
fxy=80xy3105x2y4 f_{xy} = 80xy^3 - 105x^2y^4
The second-order mixed partial derivative fxy f_{xy} is:
80xy3105x2y4 \boxed{80xy^3 - 105x^2y^4}

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