Find the Derivative - d/dx natural log of e^(x^2)

Problem

d(ln(e(x2)))/d(x)

Solution

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

ln(e(x2))=x2

2. Rewrite the derivative problem using the simplified expression.

d(ln(e(x2)))/d(x)=d(x2)/d(x)

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

d(x2)/d(x)=2*x

Final Answer

d(ln(e(x2)))/d(x)=2*x

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