Question: "Compute the derivatives indicated. g(x,y)=xe−xy,gxy(−3,2)" - Plainmath

lunnatican4

Answered question

2021-12-09

Compute the derivatives indicated.

g (x, y) = x e^{- x y}, g_{x y} (- 3, 2)

Answer & Explanation

habbocowji

Beginner2021-12-10Added 22 answers

Step 1
Given function is:

g (x, y) = x e^{- x y}

Differentiating above partially with respect to x we get,

g_{x} (x, y) = e^{- x y} - x y e^{- x y}

Differentiating above partially with respect to y we get,

g_{x y} (x, y) = - x e^{- x y} - x e^{- x y} + x^{2} y e^{- x y}

\Rightarrow g_{x y} (x, y) = (x^{2} y - 2 x) e^{- x y}

\Rightarrow g_{x y} (x, y) = x (x y - 2) e^{- x y}

Step 2
At the point (−3,2) we get,

g_{x y} (- 3, 2) = (- 3) (- 3 \cdot 2 - 2) e^{- (- 3) \cdot 2}

\Rightarrow g_{x y} (- 3, 2) = (- 3) (- 8) e^{6}

\Rightarrow g_{x y} (- 3, 2) = 24 e^{6}

Hence the answer.

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