Does The Derivative Exist (It's SHOCKING❗️)

Hey Ninjas! We're taught that the derivative of the continuous function y=abs(x) doesn't have a derivative at the origin because the absolute value function has a cuspe there. But in this video, if we multiply the absolute value function by another term x, does this change whether the derivative exists?

I uncover the details here step by step using the product rule, breaking the absolute value function down as a piecewise function, and then bridging the parts together using limits of approaching the origin from both sides to uncover the answer! Make sure to subscribe if you want more helpful tips for your Calc AB exam and smash that like button if you found this video useful. Hope you enjoy!

0:00 - Introduction
0:10 - Recap on Abs(x)
0:50 - Product Rule
1:40 - Piecewise Function Breakdown
2:47 - Derivative Function Breakdown
3:39 - Derivative Piecewise Function
4:25 - Approaching Origin (Limits)
5:37 - Finding The Answer

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