Compute the derivatives indicated. g(x, y) = xe^{−xy} , g_{xy}(−3, 2)

lunnatican4

lunnatican4

Answered question

2021-12-09

Compute the derivatives indicated.
g(x,y)=xexy,gxy(3,2)

Answer & Explanation

habbocowji

habbocowji

Beginner2021-12-10Added 22 answers

Step 1
Given function is:
g(x,y)=xexy
Differentiating above partially with respect to x we get,
gx(x,y)=exyxyexy
Differentiating above partially with respect to y we get,
gxy(x,y)=xexyxexy+x2yexy
gxy(x,y)=(x2y2x)exy
gxy(x,y)=x(xy2)exy
Step 2
At the point (−3,2) we get,
gxy(3,2)=(3)(322)e(3)2
gxy(3,2)=(3)(8)e6
gxy(3,2)=24e6
Hence the answer.

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