Find the Derivative - d/dx square root of x^2

Problem

d(√(,x2))/d(x)

Solution

1. Simplify the expression before differentiating by noting that the square root of a squared variable is the absolute value of that variable.

√(,x2)=|x|

2. Identify the derivative of the absolute value function |x| which is defined for all x≠0

d(x)/d(x)=x/|x|

3. Rewrite the result using the original radical notation if preferred, noting that |x|=√(,x2)

x/|x|=x/√(,x2)

Final Answer

d(√(,x2))/d(x)=x/√(,x2)

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