Find the 2nd Derivative e^(2x)

Problem

d2(e(2*x))/(d(x)2)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=e(2*x)

2. Apply the chain rule for the first derivative, where d(eu)/d(x)=eu⋅d(u)/d(x) with u=2*x

3. Calculate the first derivative.

d(e(2*x))/d(x)=e(2*x)⋅2

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

4. Apply the chain rule again to the first derivative to find the second derivative.

d2(e(2*x))/(d(x)2)=(d(2)*e(2*x))/d(x)

d2(e(2*x))/(d(x)2)=2⋅(e(2*x)⋅2)

5. Simplify the resulting expression by multiplying the constants.

d2(e(2*x))/(d(x)2)=4*e(2*x)

Final Answer

d2(e(2*x))/(d(x)2)=4*e(2*x)

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