Derivative of modulus of a function

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SUMMARY

The derivative of the modulus of a function can be calculated using the formula |f(x)| = f(x) * sign(f(x)). This approach allows the application of the product rule for differentiation, with the caveat that the derivative does not exist at points where f(x) = 0 unless the derivative of f(x) itself is also zero. The discussion highlights the importance of specifying whether the function is real or complex when considering derivatives.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the product rule in calculus.
  • Knowledge of the sign function and its properties.
  • Basic concepts of real and complex variables in mathematics.
NEXT STEPS
  • Study the product rule in calculus in more depth.
  • Learn about the properties and applications of the sign function.
  • Explore the differentiation of piecewise functions.
  • Investigate the implications of derivatives in real versus complex analysis.
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Students and professionals in mathematics, particularly those studying calculus, as well as anyone interested in the differentiation of functions involving absolute values.

nil1996
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how do we take derivative of modulus of a function??
 
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hi nil1996! :smile:

|f(x)| = f(x) times sign(f(x))

so you can use the product rule, except where f(x) = 0 (where |f|' won't exist unless f' = 0) :wink:
 
Are you talking about a function of a real or complex variable?
 

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