Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.
Sagot :
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
The gradient vector field of a function
Suppose that a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.
In which:
fx(x,y) is the partial derivative of f relative to variable x.
fy(x,y) is the partial derivative of f relative to variable y.
The function in this problem is defined as follows:
f(x,y) = xe^(9xy).
The partial derivative relative to x as follows:
fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).
The partial derivative relative to y as follows:
fy(x,y) = 9x²e^(9xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
To learn more about Gradient Function visit:
brainly.com/question/13646769
#SPJ4
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.
