Multivariate Differentiation on Composite Functions

Asked May 16 '13 at 02:30

Active May 16 '13 at 03:34

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Given $F(x,y,z) = (f(x,y,z),g(x,y,z),f(x,y,z) + g(x,y,z))$ I'm a little confused about what the derivative matrix would be.

Is it the 3 by 3 matrix $(DF_1, DF_2, DF_3)$ where $DF_1 = (\frac{\partial f}{\partial x} \;\; \frac{\partial f}{\partial y} \;\; \frac{\partial f}{\partial z})$ and similarly for $DF_2$ and $DF_3$ ?

Thanks.

edited May 16 '13 at 03:34

asked May 16 '13 at 02:30

N4v

1

Yes, except $DF_2$ would be $\nabla g$ and $DF_3 = DF_1 + DF_2$. – John Douma May 16 '13 at 04:33

Multivariate Differentiation on Composite Functions

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