Question

Given f(x; y) = e^x cos y + 2xy^2, determine the partial derivatives fxx, fxy and fxyy.

Answer 1

f_x =
is just derivative with respect to x pretending every other variable is a constant,

Answer 2

the first is just the second derivative wrt x, leaving y as a constant.

Answer 3

You know how to find f' if \[f=e^x cos(3)+2x(cos(3))^2 \]
don't you?

Answer 4

the second is obtained by taking the derivative wrt x first and then taking the derivative of the result wrt y.

Answer 5

and so on...

Answer 6

for fxx i got \[e ^{x}Cos y\]

Answer 7

for fxy i got \[- e ^{x}\sin y + 4 y\]

Answer 8

for f xyy i got \[4-e ^{x} \cos y\]

Answer 9

not too sure of my answers

Answer 10

fxx is right

Answer 11

fxy is right

Answer 12

fxyy is good too