Find the Derivative - d/dx square root of natural log of x

Problem

d(√(,ln(x)))/d(x)

Solution

1. Identify the outer and inner functions to apply the chain rule. The expression is of the form u(1/2) where u=ln(x)

2. Apply the power rule to the outer square root function. The derivative of √(,u) is 1/(2√(,u))

3. Apply the chain rule by multiplying the result by the derivative of the inner function, ln(x)

4. Differentiate the inner function. The derivative of ln(x) is 1/x

5. Simplify the resulting expression by combining the terms into a single fraction.

Final Answer

d(√(,ln(x)))/d(x)=1/(2*x√(,ln(x)))

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