Hey friends! I am having a slight confusion as to finding the points of non differentiability of sum, product and composite of functions.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the functions f and g. If f is differentiable on an interval and so is g, then this interval comes under the domain of f+g, and f+g is also differentiable on this interval. Similarly, for product..... Now if we want to find the points of non-differentiability of f+g, we can't straightaway write all the points not included in the above interval, since we know that the function f+g is differentiable on that interval, but there is no comment about the differentiability at other points. Then how can we use this rule to find the points of non-differentiability of f+g or fg or fog????

For example, consider the function: |x||x|. Now this is fg, f:|x| & g:|x|. f, g are differentiable on all real numbers except 0. However, from the rule fg is differentiable on all R-{0}, which is true BUT NOT ONLY ON R-{0}, also at 0. Clearly we are unable to exploit the rule for the required purpose here!!!!

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# Finding points of non-differentiability

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