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Which of the following functions is differentiable at x = 0? |
$e^{|x|}+|x|^2$ $e^{|x|}-|x|^2$ $\tan(|x|)+|x|$ $\tan(|x|)-|x|$ |
$\tan(|x|)-|x|$ |
Linear combination of one differentiable and one non-differentiable function is always nondifferentiable. Hence (a) and (b) are wrong. Now, $\tan(|x|)-|x|=\frac{|x|^3}{3}+\frac{2|x|^5}{15}+.....$ is differentiable at x = 0, whereas $\tan(|x|)+|x|=2|x|+\frac{|x|^3}{3}+\frac{2|x|^5}{15}+.....$ is not differentiable at x = 0. [∵ |x| is not diff. at x = 0] |
