Math Help - Differentiable function

1. Differentiable function

By using the definition of a differentiable function, show that the following function is differentiable in (2,2):

f(x,y) = e^[x + 2y]

Thx!!

2. Re: Differentiable function

Originally Posted by marqushogas
By using the definition of a differentiable function, show that the following function is differentiable in (2,2):

f(x,y) = e^[x + 2y]

Thx!!
Well, what is the definition of differentiability?

3. Re: Differentiable function

In two variables: If a function f(x,y) is differentiable in (a,b) there exists two numbers, A and B, and a function r(h,k) such that:

f(a+h,b+k) - f(a,b) = A*h + B*k + sqrt(h^2+k^2)*r(h,k) and r(h,k) -> 0 when (h,k) -> (0,0)