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Answer to Question #10414 in Calculus for Taher Ali Habib
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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Thank You so much. :) I completely forgot the fact that conditions may either be necessary or sufficient
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