Note the derivative rule
[tex]\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)[/tex]
