|x| is a tricky one, since it changes at x=0. Consider it a |x| = √x^2. Then, using the chain rule,
d/dx √x^2 = 2x/(2√(x^2)) = x/|x|
Note that this correctly captures the change of slope at x=0.
d/dx[5(x^2 + 3|x|)]
= 5(2x + 3x/|x|)
Also, the function is not differentiable at x=0.
Evaluate the given expression:
d/dx[5(x^2 + 3|x|)]
Any help with this is appreciated!
2 answers
Thank you!