Question

Let g(x, y, z) = e^(x)y + z ln(y). Calculate the gradient of g.

Answer 1

what are the partials ?

Answer 2

dg/dx

dg/dy

dg/dz

those :)

Answer 3

i calculate each of the partials and thats the gradient?

Answer 4

yes

Answer 5

http://betterexplained.com/articles/vector-calculus-understanding-the-gradient/

Answer 6

so like dg/dx is e^x*y etc

Answer 7

g(x,y,z) = e^(x)y + z ln(y)

dg/dx = y e^x(y) + 0 ;consider all other variables as a constant

Answer 8

e^(x)2 derives to: 2 e^(x)2 if I see it right

Answer 9

if its: (e^x)y then it derives to (e^x)y ..

Answer 10

(e^(x))*y + z ln y. its e raised to the x times y

Answer 11

ahhhh

then in dg/dx, treat all variable that are not "x" as a constant

dg/dy

Answer 12

dg/dx = y (e^x) + 0

dg/dy = e^x + z/y

dg/dz = 0 + ln(y)

Answer 13

gotcha!

Answer 14

the gradient can be expressed as an equation that combines all these or as a vector of the form <dg/dx, dg/dy, dg/dz>

Answer 15

Well, it's not technically an equation but a summation of vectors to define a further vector.