What is the first derivative of modulus function?

Answer 1

f(x)=|x|

|x| = sqrt(x^2)

f(x) = sqrt (x^2)

f'(x)=1/2sqrt(x^2) d/dx(x^2)

f'(x) = 2x /2sqrt(x^2)

f'(x) = x/sqrt(x^2)

f'(x)= x /|x|

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Note: d/dx [sqrt(x^2] = d/dx [x^(1/2)] =(1/2)x^(-1/2)=1/2x^(1/2)=1/2sqrt(x)