Question #10414

If F(x)〓x.x and G(x)〓|x|, then both FoG and GoF are differentiable at x〓0 being equal to x.x (or x squared). But G(x) is not differentiable at x〓0. Does this contradict the chain rule requirements where both the functions must be differentiable at their respective domain points?

Expert's answer

It doesn't contradict, because the condition in rule is sufficient, so if it's

held the superposition will be differentiable. If it's not held, we can't

definitely say something about the result it may be differentiable or may not,

it depends on certain functions.

held the superposition will be differentiable. If it's not held, we can't

definitely say something about the result it may be differentiable or may not,

it depends on certain functions.

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Assignment Expert07.08.13, 17:24You're welcome. We are glad to be helpful.

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Taher Ali Habib30.07.13, 14:15Thank You so much. :) I completely forgot the fact that conditions may either be necessary or sufficient

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