Find the Derivative - d/dx natural log of e^(4x)

Problem

d(ln(e(4*x)))/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(e(4*x))=4*x

2. Rewrite the derivative problem using the simplified expression.

d(ln(e(4*x)))/d(x)=(d(4)*x)/d(x)

3. Apply the power rule for differentiation, which states that (d(a)*x)/d(x)=a

(d(4)*x)/d(x)=4

Final Answer

d(ln(e(4*x)))/d(x)=4

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