Precalculus

Evaluate the given expression:
d/dx[5(x^2 + 3|x|)]

Any help with this is appreciated!

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  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.

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  2. Thank you!

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