Let and be mappings. Prove that their composition is a differentiable mapping. (Take for simplicity). Then show that .

I do not know how to prove this and would appreciate some help. Thanks!

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- Feb 17th 2011, 12:02 AMZenniecomposition of mappings
Let and be mappings. Prove that their composition is a differentiable mapping. (Take for simplicity). Then show that .

I do not know how to prove this and would appreciate some help. Thanks! - Feb 17th 2011, 05:59 AMHallsofIvy
The first thing you should know is that you

**can't**prove it. What you have stated is untrue. The composition of two arbitrary mappings is NOT in general a**differentiable**mapping.

Did you mean to say that F and G are themselves differentiable mappings? What is your definiton of "differentiable"?