Question

Find the partial derivative of f(x,y)=(3x+3y)e^y

Answer 1

y'[x] == (-3 E^y + Derivative[1, 0][f][x, y])/(3 E^y + 3 E^y x + 3 E^y y - Derivative[0, 1][f][x, y])

Answer 2

\[f_x=3e^y\]

\[f_y=(3x+3y)e^y+3e^y\]

Answer 3

f'x = 3e^y(3x+3y)

f'y = 3e^y(3x+3y)

Answer 4

why dn't you just multpply them out... i beleive that zarkon is correct

Answer 5

i am ;)

Answer 6

outside inside rule e^y will stay e^y always, leave inside then multiply inside respect to x and y.

Answer 7

zarkon is probably right though go with zarkon.

Answer 8

if you multiply it out Goat you get

3xe^y+3ye^y

fx =3e^y + 0
fy=3xe^y+3e^y=3e^y(x+1)

Answer 9

could be errors but i just did that without paper

Answer 10

use the product rule for fy

Answer 11

ahh yes both y's so yeah

Answer 12

but the first is correct

Answer 13

yep i see thanks i am working on my understanding of this as well.

Answer 14

so how would I find fxx and fyy

Answer 15

just take the derivative again

Answer 16

\[f_{xx}=0\]
\[f_{yy}=(3y+3x+6)e^y\]

Answer 17

and fxy = 3e^y?

Answer 18

yes

Answer 19

thank you!