Find the Derivative - d/dx y=|x|
Problem
Solution
Identify the definition of the absolute value function. The function
|x| is defined piecewise asx forx>0 and−x forx<0 Differentiate each piece of the function separately. For
x>0 the derivative ofx is1 Forx<0 the derivative of−x is−1 Express the result using the signum function, denoted as
sgn(x) which returns1 for positive values and−1 for negative values.Note that the derivative does not exist at
x=0 because the left-hand limit of the derivative is−1 and the right-hand limit is1 Rewrite the derivative in a compact algebraic form using the relationship
sgn(x)=x/|x| forx≠0
Final Answer
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