Find the Derivative - d/dx natural log of e^x

Problem

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

Solution

1. Simplify the expression using the properties of logarithms. Since the natural logarithm and the exponential function are inverses, ln(eu)=u

ln(ex)=x

2. Rewrite the derivative problem using the simplified expression.

d(ln(ex))/d(x)=d(x)/d(x)

3. Apply the power rule for differentiation, which states that d(xn)/d(x)=n*x(n−1) For n=1 the derivative is 1.

d(x)/d(x)=1

Final Answer

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

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