Find the Derivative - d/dx natural log of x+3

Problem

d(ln(x+3))/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 Chain Rule which states that the derivative of ln(u) is 1/u⋅d(u)/d(x)

3. Substitute u=x+3 into the formula, resulting in 1/(x+3)⋅d(x+3)/d(x)

4. Differentiate the inner function x+3 with respect to x which equals 1

5. Simplify the expression by multiplying the terms.

Final Answer

d(ln(x+3))/d(x)=1/(x+3)

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