Find the Derivative - d/dx y=1/( natural log of x)

Problem

d()/d(x)1/ln(x)

Solution

1. Identify the function as a composition or a quotient. We can rewrite the expression using a negative exponent as (ln(x))(−1)

2. Apply the power rule and the chain rule. The derivative of un is n*u(n−1)⋅d(u)/d(x)

3. Differentiate the outer function, which gives −1*(ln(x))(−2)

4. Differentiate the inner function ln(x) which is 1/x

5. Multiply the results together to find the final derivative.

6. Simplify the expression by moving the negative exponent to the denominator.

Final Answer

d()/d(x)1/ln(x)=−1/(x*(ln(x))2)

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