Find the gradient vector field of f(x, y) = xe^{3xy}.

Weltideepq

Weltideepq

Answered question

2021-11-11

Find the gradient vector field of f(x,y)=xe3xy.

Answer & Explanation

Aretha Frazier

Aretha Frazier

Beginner2021-11-12Added 16 answers

Given function,
f(x,y)=xe3xy
Gradient vector field is given by,
f=dfdxi×dfdyj
f=ddx(xe3xy)i+ddy(xe3xy)j
Using product rule
f=xddx(e3xy)i+e3xyddx(x)i+xddy(e3xy}j
f=xe3xyddx(3xy)i+e3xyi+xe3xyddy(3xy)j
f=(3x+1)e3xyi+3x2e3xyj

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