Question

v(x,y)=(y^2cos(xy^2)+ye^x, 2xycos(xy^2)+e^x)

Find a function f such that v=grad f

Answer 1

is it not take integral of v?

Answer 2

@cinar

Answer 3

@Zizik v = grad f, it means v = gradient f, right?

Answer 4

yes

Answer 5

v(x,y) = (partial derivative of x, partial derivative of y)

Answer 6

yes, taking integrals.

Answer 7

\[f=\sin(xy^2)+ye^x\]

Answer 8

\[\int\limits_{}^{}v(x,y)dx=\sin(xy^2)+ye^x+c_{1}(y)\\\ \int\limits_{}^{}v(x,y)dy=\sin(xy^2)+c_{1}(x)\]