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enter image description hereSo I am running into this question, and I am not sure if desmos is wrong in this case.

The question is true or false:

If f · g and g is differentiable at x = a, then f is differentiable at x = a.

A counter example would be: g(x) = 0 f(x) = |x| So f(x)*g(x) = 0.

Therefore g'(x) = 0, f'(x) = undefined, (f*g)'(x) = 0

But according to desmos this doesn't work and the derivative of f*g is undefined, I am looking for insight about whether this statement is true or false.

1 Answers1

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Such statement is false in general. Just consider $f(x) = x^{-1}$, $g(x) = x$ and $a = 0$.

user0102
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  • Any idea why according to desmos this example does not work? –  Nov 10 '19 at 22:57
  • Maybe it is because $f$ is not defined at $0$, so the given software does not recognize $h(x)$ as a function defined over the reals. – user0102 Nov 10 '19 at 22:59