If u-ax2-2hxy-by2- then x-2u- x- y-y-2u- y2-

The correct option is A 2(hx+by) ∂ u∂ #10;x=2ax+2hy d^2u∂ x∂ y=2h ∂ u∂ y=2hx+2by d^2u∂ y^2=2b #10; xd^2u∂ #10; x∂ y+ yd^2u ...

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Higher Order Derivatives

If u=ax2+2h...

Question

If $u = a x^{2} + 2 h x y + b y^{2}$ ,

then $x \frac{\partial^{2} u}{\partial x \partial y} + y \frac{\partial^{2} u}{\partial y^{2}} = ?$

2 (h x + b y)

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2 (h x - b y)

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2 (b x + h y)

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2 (b x - h y)

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Solution

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I

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\frac{\partial^{2} u}{\partial x \partial y} = \frac{\partial^{2} u}{\partial y \partial x}

u = x^{3} - 3 x^{2} y + y^{3}

x \frac{\partial^{2} u}{\partial x^{2}} + y \frac{\partial^{2} u}{\partial x \partial y} = ?

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