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

Problem

d(√(,x))/d(x)

Solution

1. Rewrite the square root function using a fractional exponent to prepare for differentiation.

√(,x)=x(1/2)

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

d(x(1/2))/d(x)=1/2*x(1/2−1)

3. Simplify the exponent by performing the subtraction.

1/2*x(1/2−1)=1/2*x(−1/2)

4. Rewrite the expression using positive exponents and radical notation for the final form.

1/2*x(−1/2)=1/(2*x(1/2))

1/(2*x(1/2))=1/(2√(,x))

Final Answer

d(√(,x))/d(x)=1/(2√(,x))

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