Evaluate the given expression:

Question

d/dx[5(x^2 + 3|x|)]

Any help with this is appreciated!

Answer 1

|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.

Answer 2

Thank you!