Find the 2nd Derivative e^x

Problem

d2(ex)/(d(x)2)

Solution

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

2. Find the first derivative by applying the rule for the natural exponential function, where d(ex)/d(x)=ex

3. Differentiate again to find the second derivative by applying the same rule to the result of the first derivative.

4. Conclude that the derivative of ex remains ex regardless of the order of differentiation.

Final Answer

d2(ex)/(d(x)2)=ex

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