Question

How do you differentiate `(e^ (2x) - e^(-2x) ) ^ 2`?

Answer 1

`4(e^{4x}-e^{-4x})`

Explanation:

First, differentiate "something" squared as `2xx` something. Then multiply by whatever you get by differentiating the something:
#2(e^{2x}-e^{-2z})^1xx d/{dx}(e^{2x}-e^{-2x}) =2(e^{2x}-e^{-2z})xx(2e^{2x}+2e^{-2x})# (because `d/dx(e^{ax})=ae^{ax}`)
`=4(e^{2x}-e^{-2x})(e^{2x}+e^{-2x})`.
Remember `(a-b)(a+b)=(a^2-b^2)` and `e^{2x}xxe^{2x}=e^{4x}`