Find the Derivative - d/dx ( natural log of x)^2

Problem

d(ln(x))/d(x)

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The outer function is u2 and the inner function is u=ln(x)

2. Apply the Power Rule to the outer function by bringing the exponent to the front and subtracting one from the exponent.

2*(ln(x))(2−1)

3. Multiply by the derivative of the inner function, ln(x) according to the Chain Rule.

d(ln(x))/d(x)=2*ln(x)⋅d(ln(x))/d(x)

4. Differentiate the natural log function, where the derivative of ln(x) is 1/x

d(ln(x))/d(x)=2*ln(x)⋅1/x

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

d(ln(x))/d(x)=(2*ln(x))/x

Final Answer

d(ln(x))/d(x)=(2*ln(x))/x

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