How do I find the Taylor series for a function with multiple variables?

[Felesinho]

Homework Statement

I required to make a perturbation expansion in ε of the function:

Homework Equations

A(X,y,z)=A(x-εsin(wy),y,z).
X=x-εsin(wy)

The Attempt at a Solution

Solution:
A(X,y,z)=A₀(X,z)+ε[A₁(X,z)+∂/∂XA₀(X,z)]sin(wy)+o(ε^2)
I get the terms A₀(X,z) and ∂/∂XA₀(X,z)sin(w,y) with the derivative with respect to ε . But I could not get A₁.
Thanks

 

[MathematicalPhysicist]

Can you elaborate on this?

Do you want to find a Taylor series for this function?

In that case you've got the formula for Taylor series in more than one variables.