Find the Derivative - d/dx natural log of 1+x

Problem

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

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, requiring the use of the chain rule.

2. Apply the rule for the derivative of ln(u) which is 1/u⋅d(u)/d(x)

3. Substitute u=1+x into the formula.

4. Differentiate the inner function 1+x with respect to x which results in 1

5. Multiply the results to find the final derivative.

Final Answer

d(ln(1+x))/d(x)=1/(1+x)

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