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x -x e, e both
x x We know the derivative of e is again e (i.e itself) x d x x First derivative of e = --- e = e dx x d x Second derivative of e = --- e dx
Therefore e^x is the function whose 2nd derivative is itself.
-x -x We know the derivative of e is again -e -x d -x -x First derivative of e = --- e = -e dx -x d -x -x Second derivative of e = --- -e = e dx
Therefore e^-x is the function whose 2nd derivative also is itself.Therefore e^x and e^-x both's 2nd derivative is equal to the function itself.