Question

="f(x) = 2^{x + 1} - 2^{x - 1} " alt="f(x) = 2^{x + 1} - 2^{x - 1} " align="absmiddle" class="latex-formula">
please help, we need to find the derivative, explain step by step ​

Answer 1

Note the derivative rule

$\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}$

Let's see

$\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})$

$\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}$

$\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}$

$\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}$

$\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2$

$\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}$

$\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})$

$\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)$