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Math Help - Chain Rule Question

  1. #1
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    Chain Rule Question

    This one comes in two parts, but is basically the same question:

    a) If f(x)= \rvert \sin x \lvert, find f'(x) and sketch the graphs of f and f'. Where is f not differentiable?

    b) a) If g(x)= \sin \rvert x \lvert, find g'(x) and sketch the graphs of g and g'. Where is f not differentiable?

    So, I believe that f'(x)= \rvert \cos x \lvert and g'(x)= \cos \rvert x\lvert, and know how to graph each of these functions. What I am not confident on is the part about where are these functions not differentiable? As I look at the graphs, it looks to me like they are both differentiable across all real numbers. Am I missing something?
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  2. #2
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    They are not differentiable across all real numbers becasue they have sharp corner curves or 'cusps'.

    For the first function these appear at the zeros of \sin x

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  3. #3
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    I follow the rule of not being differentiable at sharp corners. Maybe my graph is too small to tell, but I didn't realize that there were sharp corners at the zeros of \vert \sin x\vert '

    Thanks for your help. I appreciate it.
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