Find the 2nd Derivative e^x

Problem

d^2(e^x)/(d(x)^2)

Solution

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

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

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 e^x remains e^x regardless of the order of differentiation.

Final Answer

d^2(e^x)/(d(x)^2)=e^x

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