Question

Dear all, I am looking to differentiate x(d/dy) * z(d/dx) . Which rule for differentiation should I use?
Thanks

Answer 1

Chain rule?
d / dx = d / dy • dy / dx

Answer 2

Sorry but where does the z go?

x(d/dy)*z*(d/dx)

Answer 3

By x(d / dy) do you mean the multiplication of x with d / dy or you mean taking the derivative of x with respect to y?

Answer 4

multiplication: the entire expression looks as such:

xd/dy(zd/dx-xd/dz) - yd/dx - yd/dx*xd/dz +y(d/dz + xd/dxd/dz)

Answer 5

xd / dxd / dz?

Answer 6

yes, xd^2/dxdz

Answer 7

second differential of x in repsect to x and z

Answer 8

Try this
Move all the d in front, example
xd change to dx and see if you can simplify it

Answer 9

is it "legal" ? I am working with commutability of operators, and their sequence is pivotal for complementarity. However, I have not worked with partial differentiation in respecet to several dimensions, and of a variable foreign to the dimensions, so I am not sure. For instance, what is the simple rule for differentiation p*d/du, where p and u designate two different dimensions?

Answer 10

knowing that could help...

Answer 11

I am not sure but you could try doing that first

Answer 12

ok am trying

Answer 13

Hmm I am not sure... as x*(d/dy) * z*(d/dx) is given, it means differentiate first x with respect to y, and multiply that to the derivative of z with respect to x.

Answer 14

@sem well, what you can apply is the product rule...there is a product
so you just need to apply the product rule for it
are you familiar with it ?

Answer 15

Yes, its (uv)' = u'v + v'u ?

Answer 16

perfect

Answer 17

How do you apply that to the case of x(d/dy)*z(d/dx) ?

Answer 18

that is what you have to apply it :)

Answer 19

The operator d/dy perfoms an operation on x, however I am not sure how to solve x*d/dy