Question

Compute the matrix of the partial derivative: f(x,y) = (e^x, sinxy)

Answer 1

Matrix ?? Only if it is second order.
Otherwise just a 2-vector

Answer 2

so would i have to use the derivative as the second row?
{e^x sinxy
e^x ycosxy} ?

Answer 3

Ahh sorry u r right -

Answer 4

did i derive them correctly? that's usually where I start to mess up

Answer 5

It's a matric since u have TWO diffrent functions in the F

Answer 6

No - there must be on ZERO result because the first component e^x is independent of y

Answer 7

sorry, but I don't know what you mean. I am more of a visual learner. Could I use the Dot Product to solve this?

Answer 8

Yes - but "dot product " with a vector-differential operator

Answer 9

Nabla = (Dx, Dy)

Answer 10

Nabla?

Answer 11

Grad (more common in US)

Answer 12

gradient?

Answer 13

You see Grad is a notation for the operation. Gradient is the opertaion. Grad is the notation (like + is the notation for addition)

Answer 14

So anyways in ur matrix
First Column = Grad (e^x), Second Column= Grad(sin xy)

Answer 15

so i should have grad = < e^x , xcos(xy) >?

Answer 16

Noo
1-st column is Grad(e^x) is A COLUMN of 2 derivatives i.e. Dx above Dy
2-nd column Grad(sin xy) ....

Answer 17

{e^x xcosxy
0 ycosxy} ? ( am I getting close at all? )

Answer 18

Yes u r there

Answer 19

Sorry, the second column is inverted in order

Answer 20

?

Answer 21

invert the order in the 2-nd column

Answer 22

i'm sorry, I don't quite know what you mean by 'invert.' do i switch them? or change them to negative?

Answer 23

@Mikael Sorry if I'm a but slow at this