Can the product rule be applied if one of the functions is not differentiable? For example,(adsbygoogle = window.adsbygoogle || []).push({});

f(x)={g(x)sin(1/x), x not =0

=0, x=0

where g(0)=g'(0)=0.

f'(0)=g'(0)sin(1/0) + g(0)dsin(1/x)/dx

=0sin1/0+0dsin(1/x)/dx=0?

applying the limit definition, I get

f'(0)=g'(0)lim sin(1/h) where h-->0

is this zero?

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

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!

# Product rule

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