- #1

smerhej

- 20

- 0

## Homework Statement

Let

*f(u,v)*be an infinitely differentiable function of two variables, and let

*g(x,y) = (x^2 + y^4, xy)*. If f[itex]_{v}[/itex] (5,2) = 1, f[itex]_{uu}[/itex] (5,2) = 2, f[itex]_{vv}[/itex] (5,2) = -2 and f[itex]_{uv}[/itex] (5,2) = 1, computer d^2(f o g)/dxdy at (2,1)

## Homework Equations

The Chain Rule

## The Attempt at a Solution

I set u = x^2 + y^4 and v = xy . Differentiating df/dx gives 2x(df/du) + y(df/dv) .[ df/dy gives 4y^3(df/du) + x(df/dv) but I don't think that's relevant ]. My idea from there was to use the results stated in the question to fill in these unknown derivatives.

Thanks!