Find the 2nd Derivative 1/x

Problem

d2()/(d(x)2)1/x

Solution

1. Rewrite the expression using a negative exponent to make differentiation easier.

1/x=x(−1)

2. Find the first derivative by applying the power rule, which states d(xn)/d(x)=n*x(n−1)

d(x(−1))/d(x)=−1*x(−2)

3. Find the second derivative by differentiating the first derivative again using the power rule.

(d(−)*x(−2))/d(x)=(−2)*(−1)*x(−3)

4. Simplify the expression and rewrite it with a positive exponent.

2*x(−3)=2/(x3)

Final Answer

d2()/(d(x)2)1/x=2/(x3)

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