Question

What is the second derivative of #f(x)=(e^x + e^-x) / 2 #?

Answer 1

`f''(x) = f(x)`

Explanation:

`f(x) = 1/2(e^x+e^-x)`

`f'(x) = 1/2 (e^x-e^-x)` `" "` `("use "d/dx(e^u) = e^u (du)/dx)`

`f''(x) = 1/2(e^x+e^-x) = f(x)`