Find the Derivative Using Chain Rule - d/dx f(x) = square root of x

Problem

d(√(,x))/d(x)

Solution

1. Rewrite the square root function as a power using the identity √(,x)=x^(1/2)

2. Apply the power rule for derivatives, which states that d(x^n)/d(x)=n*x^(n−1)

3. Substitute n=1/2 into the power rule formula.

4. Simplify the exponent by calculating 1/2−1=−1/2

5. Rewrite the expression using positive exponents and radical notation, noting that x^(−1/2)=1/√(,x)

Final Answer

d(√(,x))/d(x)=1/(2√(,x))

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