I am working my lonely way through Spivack's "Calculus on Manifolds." (not a registered student anywhere, alas).(adsbygoogle = window.adsbygoogle || []).push({});

On p. 23 is a set of problems involving the inner product. I believe I've got it up to d), which asks for a function f:R->R s.t. f is differentiable but |f| is not differentiable.

I believe that |f| is not differentiable for f(x)=x. (if that's wrong I have to start the book all over).

I'm having trouble seeing how to reach this conclusion from consideration of the inner product. |f|**2 = <f,f>, and for g= <f,f>, g' = <x,1> + <1,x>,

F = g**(1/2) = |f|,

and if this is ok so far, I would expect something to be wrong with the next calculation:

F' =(1/2)g**(-1/2)(g') = (1/2)(x**2)**(-1/2) (2x) = 1.

Please help me understand what I've done wrong here. thanks

Ken C

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inner Product

**Physics Forums | Science Articles, Homework Help, Discussion**