Find the 2nd Derivative f(x) = natural log of x

Problem

ƒ(x)=ln(x)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=ln(x)

2. Find the first derivative by applying the power rule for logarithms, where d(ln(x))/d(x)=1/x

3. Rewrite the first derivative as a power to prepare for the next differentiation: ƒ(x)′=x(−1)

4. Find the second derivative by applying the power rule d(xn)/d(x)=n*x(n−1) to x(−1)

5. Simplify the resulting expression ƒ(x)″=−1*x(−2) by moving the variable back to the denominator.

Final Answer

d2(ln(x))/(d(x)2)=−1/(x2)

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