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

Problem

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

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, which requires the use of the Chain Rule.

2. Apply the formula for the derivative of the natural logarithm, which states d(ln(u))/d(x)=1/u⋅d(u)/d(x)

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

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

5. Simplify the expression by multiplying the terms.

Final Answer

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

Want more problems? Check here!