Find the Derivative - d/dx 1/(2 square root of x)

Problem

d()/d(x)1/(2√(,x))

Solution

1. Rewrite the expression using exponent notation to make it easier to differentiate.

1/(2√(,x))=1/(2*x(1/2))

2. Apply the properties of exponents to move the variable to the numerator.

1/2*x(−1/2)

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

d()/d(x)1/2*x(−1/2)=1/2⋅(−1/2)*x(−1/2−1)

4. Simplify the coefficient and the exponent.

−1/4*x(−3/2)

5. Convert the expression back into radical form for the final result.

−1/(4*x(3/2))=−1/(4√(,x3))

Final Answer

d()/d(x)1/(2√(,x))=−1/(4*x√(,x))

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