Find the Derivative - d/dx natural log of e^(5x)

Problem

d(ln(e(5*x)))/d(x)

Solution

1. Simplify the expression using the property of logarithms that states ln(eu)=u

2. Substitute the simplified expression back into the derivative operator.

ln(e(5*x))=5*x

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

(d(5)*x)/d(x)=5

Final Answer

d(ln(e(5*x)))/d(x)=5

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