IDNLearn.com offers a comprehensive solution for finding accurate answers quickly. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.
Sagot :
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
How to obtain the gradient vector field of a function?
Suppose that we have 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.
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^(3xy).
Applying the product rule, the partial derivative relative to x is given as follows:
fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).
Applying the chain rule, the partial derivative relative to y is given as follows:
fy(x,y) = 3x²e^(3xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
More can be learned about the gradient vector field of a function at https://brainly.com/question/25573309
#SPJ1
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. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.
